the 29 isometry classes of irreducible [23,7,9]_2 codes are:

code no       1:
================
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0
1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 1 0 0 0
1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0
0 0 1 1 0 1 0 1 0 1 1 0 1 0 0 1 0 0 0 0 0 1 0
0 1 1 0 0 0 1 1 1 0 0 1 0 1 0 1 0 0 0 0 0 0 1
the automorphism group has order 1
and is strongly generated by the following 0 elements:
(
)
acting on the columns of the generator matrix as follows (in order):
orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 }, { 13 }, { 14 }, { 15 }, { 16 }, { 17 }, { 18 }, { 19 }, { 20 }, { 21 }, { 22 }, { 23 }

code no       2:
================
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0
1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 1 0 0 0
1 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0
1 0 1 1 0 1 0 1 0 1 1 0 1 0 0 1 0 0 0 0 0 1 0
1 0 1 0 0 0 1 1 1 0 0 1 0 1 0 1 0 0 0 0 0 0 1
the automorphism group has order 2
and is strongly generated by the following 1 elements:
(
1 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 
1 0 1 0 0 0 1 1 1 0 0 1 0 1 0 1 
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 
1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 
1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(1, 21)(2, 8)(3, 17)(4, 10)(5, 18)(6, 9)(7, 23)(11, 14)(15, 20)(16, 19)
orbits: { 1, 21 }, { 2, 8 }, { 3, 17 }, { 4, 10 }, { 5, 18 }, { 6, 9 }, { 7, 23 }, { 11, 14 }, { 12 }, { 13 }, { 15, 20 }, { 16, 19 }, { 22 }

code no       3:
================
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0
1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 1 0 0 0
0 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0
1 0 1 0 0 0 1 1 0 1 0 1 0 1 1 0 0 0 0 0 0 1 0
0 1 0 0 1 0 1 1 0 1 1 0 1 0 0 1 0 0 0 0 0 0 1
the automorphism group has order 2
and is strongly generated by the following 1 elements:
(
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 
0 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 
1 0 1 0 0 0 1 1 0 1 0 1 0 1 1 0 
1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 
1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 
0 1 0 0 1 0 1 1 0 1 1 0 1 0 0 1 
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(1, 15)(2, 6)(3, 7)(4, 21)(5, 17)(8, 22)(9, 19)(10, 14)(11, 20)(13, 23)(16, 18)
orbits: { 1, 15 }, { 2, 6 }, { 3, 7 }, { 4, 21 }, { 5, 17 }, { 8, 22 }, { 9, 19 }, { 10, 14 }, { 11, 20 }, { 12 }, { 13, 23 }, { 16, 18 }

code no       4:
================
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0
1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 1 0 0 0
0 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0
1 0 1 0 0 0 1 1 0 1 0 1 0 1 1 0 0 0 0 0 0 1 0
1 0 1 0 1 1 1 0 1 0 0 1 0 1 0 1 0 0 0 0 0 0 1
the automorphism group has order 1
and is strongly generated by the following 0 elements:
(
)
acting on the columns of the generator matrix as follows (in order):
orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 }, { 13 }, { 14 }, { 15 }, { 16 }, { 17 }, { 18 }, { 19 }, { 20 }, { 21 }, { 22 }, { 23 }

code no       5:
================
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0
1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 1 0 0 0
0 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0
1 0 1 0 0 0 1 1 0 1 0 1 0 1 1 0 0 0 0 0 0 1 0
1 0 1 0 0 1 1 0 1 0 1 1 0 1 0 1 0 0 0 0 0 0 1
the automorphism group has order 2
and is strongly generated by the following 1 elements:
(
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 
1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 
1 0 1 0 0 0 1 1 0 1 0 1 0 1 1 0 
1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 
1 0 1 0 0 1 1 0 1 0 1 1 0 1 0 1 
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 
0 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(1, 4)(2, 10)(3, 11)(5, 16)(6, 14)(7, 20)(8, 22)(9, 19)(13, 23)(15, 21)(17, 18)
orbits: { 1, 4 }, { 2, 10 }, { 3, 11 }, { 5, 16 }, { 6, 14 }, { 7, 20 }, { 8, 22 }, { 9, 19 }, { 12 }, { 13, 23 }, { 15, 21 }, { 17, 18 }

code no       6:
================
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0
1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 1 0 0 0
0 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0
1 0 1 0 1 0 0 1 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0
1 0 1 0 1 1 1 0 0 1 1 0 1 0 0 1 0 0 0 0 0 0 1
the automorphism group has order 2
and is strongly generated by the following 1 elements:
(
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(1, 3)(2, 4)(6, 7)(10, 11)(14, 15)(20, 21)
orbits: { 1, 3 }, { 2, 4 }, { 5 }, { 6, 7 }, { 8 }, { 9 }, { 10, 11 }, { 12 }, { 13 }, { 14, 15 }, { 16 }, { 17 }, { 18 }, { 19 }, { 20, 21 }, { 22 }, { 23 }

code no       7:
================
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0
1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 1 0 0 0
0 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0
1 0 1 0 1 0 0 1 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0
1 0 1 0 0 1 1 1 0 1 1 0 1 0 0 1 0 0 0 0 0 0 1
the automorphism group has order 4
and is strongly generated by the following 2 elements:
(
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
, 
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 
1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 
1 0 1 0 1 0 0 1 0 0 0 1 1 1 1 0 
1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 
0 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(1, 3)(2, 4)(6, 7)(10, 11)(14, 15)(20, 21), 
(1, 2, 3, 4)(5, 19)(6, 10, 7, 11)(8, 9)(12, 18)(13, 22)(14, 21, 15, 20)(17, 23)
orbits: { 1, 3, 4, 2 }, { 5, 19 }, { 6, 7, 11, 10 }, { 8, 9 }, { 12, 18 }, { 13, 22 }, { 14, 15, 20, 21 }, { 16 }, { 17, 23 }

code no       8:
================
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0
1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 1 0 0 0
0 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0
1 0 1 0 1 1 1 0 0 1 1 0 1 0 0 1 0 0 0 0 0 1 0
1 0 1 0 1 0 0 1 0 0 1 1 0 1 0 1 0 0 0 0 0 0 1
the automorphism group has order 1
and is strongly generated by the following 0 elements:
(
)
acting on the columns of the generator matrix as follows (in order):
orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 }, { 13 }, { 14 }, { 15 }, { 16 }, { 17 }, { 18 }, { 19 }, { 20 }, { 21 }, { 22 }, { 23 }

code no       9:
================
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0
1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 1 0 0 0
0 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0
1 0 1 0 1 1 1 0 0 1 1 0 1 0 0 1 0 0 0 0 0 1 0
1 0 1 0 1 0 0 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0 1
the automorphism group has order 2
and is strongly generated by the following 1 elements:
(
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(1, 3)(2, 4)(6, 7)(10, 11)(14, 15)(20, 21)
orbits: { 1, 3 }, { 2, 4 }, { 5 }, { 6, 7 }, { 8 }, { 9 }, { 10, 11 }, { 12 }, { 13 }, { 14, 15 }, { 16 }, { 17 }, { 18 }, { 19 }, { 20, 21 }, { 22 }, { 23 }

code no      10:
================
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0
1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 1 0 0 0
0 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0
1 0 1 0 1 1 1 0 0 1 1 0 1 0 0 1 0 0 0 0 0 1 0
1 0 1 0 1 0 0 1 0 0 0 1 0 1 1 1 0 0 0 0 0 0 1
the automorphism group has order 16
and is strongly generated by the following 4 elements:
(
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 
1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 
1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 
0 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 
1 0 1 0 1 1 1 0 0 1 1 0 1 0 0 1 
, 
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
, 
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 
, 
1 0 1 0 1 1 1 0 0 1 1 0 1 0 0 1 
1 0 1 0 1 0 0 1 0 0 0 1 0 1 1 1 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 
1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 
0 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(8, 18)(12, 19)(14, 20)(15, 21)(16, 22)(17, 23), 
(1, 3)(2, 4)(6, 7)(10, 11)(14, 15)(20, 21), 
(1, 2)(3, 4)(5, 9)(6, 10)(7, 11)(8, 12)(16, 17)(18, 19)(22, 23), 
(1, 16, 3, 22)(2, 17, 4, 23)(5, 9)(6, 8, 7, 18)(10, 12, 11, 19)(14, 20, 21, 15)
orbits: { 1, 3, 2, 22, 4, 16, 23, 17 }, { 5, 9 }, { 6, 7, 10, 18, 11, 8, 19, 12 }, { 13 }, { 14, 20, 15, 21 }

code no      11:
================
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0
1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 1 0 0 0
0 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0
1 0 1 0 1 0 1 1 0 1 1 0 0 1 0 1 0 0 0 0 0 1 0
1 0 0 1 1 1 1 0 1 0 0 1 0 0 1 1 0 0 0 0 0 0 1
the automorphism group has order 1
and is strongly generated by the following 0 elements:
(
)
acting on the columns of the generator matrix as follows (in order):
orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 }, { 13 }, { 14 }, { 15 }, { 16 }, { 17 }, { 18 }, { 19 }, { 20 }, { 21 }, { 22 }, { 23 }

code no      12:
================
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0
1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 1 0 0 0
1 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0
1 0 1 0 0 0 1 1 0 1 0 1 0 1 1 0 0 0 0 0 0 1 0
1 1 0 0 1 0 1 1 0 1 1 0 1 0 0 1 0 0 0 0 0 0 1
the automorphism group has order 1
and is strongly generated by the following 0 elements:
(
)
acting on the columns of the generator matrix as follows (in order):
orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 }, { 13 }, { 14 }, { 15 }, { 16 }, { 17 }, { 18 }, { 19 }, { 20 }, { 21 }, { 22 }, { 23 }

code no      13:
================
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0
1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 1 0 0 0
1 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0
1 0 1 0 0 0 1 1 0 1 0 1 0 1 1 0 0 0 0 0 0 1 0
1 0 0 1 0 1 1 0 1 1 0 1 1 0 0 1 0 0 0 0 0 0 1
the automorphism group has order 1
and is strongly generated by the following 0 elements:
(
)
acting on the columns of the generator matrix as follows (in order):
orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 }, { 13 }, { 14 }, { 15 }, { 16 }, { 17 }, { 18 }, { 19 }, { 20 }, { 21 }, { 22 }, { 23 }

code no      14:
================
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0
1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 1 0 0 0
1 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0
1 0 1 0 0 0 1 1 0 1 0 1 0 1 1 0 0 0 0 0 0 1 0
1 1 0 1 0 1 1 0 0 0 0 1 1 1 0 1 0 0 0 0 0 0 1
the automorphism group has order 1
and is strongly generated by the following 0 elements:
(
)
acting on the columns of the generator matrix as follows (in order):
orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 }, { 13 }, { 14 }, { 15 }, { 16 }, { 17 }, { 18 }, { 19 }, { 20 }, { 21 }, { 22 }, { 23 }

code no      15:
================
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0
1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 1 0 0 0
1 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0
1 1 1 0 0 0 1 1 0 1 0 1 0 1 1 0 0 0 0 0 0 1 0
1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 1 0 0 0 0 0 0 1
the automorphism group has order 1
and is strongly generated by the following 0 elements:
(
)
acting on the columns of the generator matrix as follows (in order):
orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 }, { 13 }, { 14 }, { 15 }, { 16 }, { 17 }, { 18 }, { 19 }, { 20 }, { 21 }, { 22 }, { 23 }

code no      16:
================
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0
1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 1 0 0 0
1 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0
1 1 1 0 0 0 1 1 0 1 0 1 0 1 1 0 0 0 0 0 0 1 0
1 1 0 1 0 1 1 0 0 0 1 1 1 0 0 1 0 0 0 0 0 0 1
the automorphism group has order 4
and is strongly generated by the following 2 elements:
(
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
1 1 0 1 0 1 1 0 0 0 1 1 1 0 0 1 
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 
1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 
1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
, 
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(1, 16)(2, 23)(3, 6)(4, 19)(5, 13)(8, 9)(10, 18)(11, 14)(12, 20)(17, 21), 
(1, 14)(2, 10)(3, 8)(4, 17)(6, 9)(7, 15)(11, 16)(18, 23)(19, 21)
orbits: { 1, 16, 14, 11 }, { 2, 23, 10, 18 }, { 3, 6, 8, 9 }, { 4, 19, 17, 21 }, { 5, 13 }, { 7, 15 }, { 12, 20 }, { 22 }

code no      17:
================
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0
1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 1 0 0 0
1 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0
1 1 1 0 0 0 1 1 0 1 0 1 0 1 1 0 0 0 0 0 0 1 0
0 1 1 0 0 1 1 0 1 0 1 1 0 1 0 1 0 0 0 0 0 0 1
the automorphism group has order 1
and is strongly generated by the following 0 elements:
(
)
acting on the columns of the generator matrix as follows (in order):
orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 }, { 13 }, { 14 }, { 15 }, { 16 }, { 17 }, { 18 }, { 19 }, { 20 }, { 21 }, { 22 }, { 23 }

code no      18:
================
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0
1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 1 0 0 0
1 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0
1 1 1 0 0 0 1 1 0 1 0 1 0 1 1 0 0 0 0 0 0 1 0
1 0 0 1 0 1 1 0 0 0 0 1 1 1 0 1 0 0 0 0 0 0 1
the automorphism group has order 1
and is strongly generated by the following 0 elements:
(
)
acting on the columns of the generator matrix as follows (in order):
orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 }, { 13 }, { 14 }, { 15 }, { 16 }, { 17 }, { 18 }, { 19 }, { 20 }, { 21 }, { 22 }, { 23 }

code no      19:
================
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0
1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 1 0 0 0
1 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0
1 1 1 0 1 0 0 1 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0
0 1 1 0 1 1 1 0 0 1 1 0 1 0 0 1 0 0 0 0 0 0 1
the automorphism group has order 2
and is strongly generated by the following 1 elements:
(
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 
1 1 1 0 1 0 0 1 0 0 0 1 1 1 1 0 
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 
0 1 1 0 1 1 1 0 0 1 1 0 1 0 0 1 
1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 
1 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(1, 9)(2, 11)(3, 10)(5, 16)(6, 7)(8, 22)(12, 19)(13, 23)(14, 20)(15, 21)(17, 18)
orbits: { 1, 9 }, { 2, 11 }, { 3, 10 }, { 4 }, { 5, 16 }, { 6, 7 }, { 8, 22 }, { 12, 19 }, { 13, 23 }, { 14, 20 }, { 15, 21 }, { 17, 18 }

code no      20:
================
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0
1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 1 0 0 0
1 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0
0 0 1 0 1 0 1 1 0 1 1 0 0 1 0 1 0 0 0 0 0 1 0
0 0 0 1 1 1 1 0 1 0 0 1 0 0 1 1 0 0 0 0 0 0 1
the automorphism group has order 1
and is strongly generated by the following 0 elements:
(
)
acting on the columns of the generator matrix as follows (in order):
orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 }, { 13 }, { 14 }, { 15 }, { 16 }, { 17 }, { 18 }, { 19 }, { 20 }, { 21 }, { 22 }, { 23 }

code no      21:
================
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0
1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 1 0 0 0
1 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0
0 0 1 0 1 0 1 1 0 1 1 0 0 1 0 1 0 0 0 0 0 1 0
0 1 1 0 1 0 0 1 1 1 0 1 0 0 1 1 0 0 0 0 0 0 1
the automorphism group has order 4
and is strongly generated by the following 2 elements:
(
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
, 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 
0 1 1 0 1 0 0 1 1 1 0 1 0 0 1 1 
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 
1 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 
1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 
1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 1 0 1 0 1 1 0 1 1 0 0 1 0 1 
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(2, 6)(3, 7)(9, 13)(10, 14)(12, 17)(19, 23), 
(1, 16)(2, 10)(3, 23)(4, 18)(5, 21)(6, 14)(7, 19)(8, 20)(9, 17)(11, 22)(12, 13)
orbits: { 1, 16 }, { 2, 6, 10, 14 }, { 3, 7, 23, 19 }, { 4, 18 }, { 5, 21 }, { 8, 20 }, { 9, 13, 17, 12 }, { 11, 22 }, { 15 }

code no      22:
================
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0
1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 1 0 0 0
1 0 1 0 0 0 1 1 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0
0 1 0 0 1 0 1 0 0 1 1 1 1 0 0 1 0 0 0 0 0 1 0
1 0 0 1 1 1 1 0 0 1 1 0 0 0 1 1 0 0 0 0 0 0 1
the automorphism group has order 1
and is strongly generated by the following 0 elements:
(
)
acting on the columns of the generator matrix as follows (in order):
orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 }, { 13 }, { 14 }, { 15 }, { 16 }, { 17 }, { 18 }, { 19 }, { 20 }, { 21 }, { 22 }, { 23 }

code no      23:
================
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0
1 1 1 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 1 0 0 0
1 1 0 1 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0
1 0 1 0 0 1 1 1 0 1 1 0 1 0 0 1 0 0 0 0 0 1 0
1 0 1 0 1 0 0 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0 1
the automorphism group has order 4
and is strongly generated by the following 2 elements:
(
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
, 
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 
)
acting on the columns of the generator matrix as follows (in order):
(1, 16)(2, 17)(3, 8)(4, 12)(5, 14)(7, 10)(9, 15)(18, 21)(19, 20), 
(1, 2)(3, 4)(5, 9)(6, 11)(7, 10)(8, 12)(14, 15)(16, 17)(18, 19)(20, 21)(22, 23)
orbits: { 1, 16, 2, 17 }, { 3, 8, 4, 12 }, { 5, 14, 9, 15 }, { 6, 11 }, { 7, 10 }, { 13 }, { 18, 21, 19, 20 }, { 22, 23 }

code no      24:
================
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0
1 1 1 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 1 0 0 0
1 0 0 0 1 1 1 0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0
1 1 0 0 1 0 1 1 0 1 0 1 0 1 1 0 0 0 0 0 0 1 0
1 0 1 0 0 1 1 0 1 0 1 1 0 1 0 1 0 0 0 0 0 0 1
the automorphism group has order 1
and is strongly generated by the following 0 elements:
(
)
acting on the columns of the generator matrix as follows (in order):
orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 }, { 13 }, { 14 }, { 15 }, { 16 }, { 17 }, { 18 }, { 19 }, { 20 }, { 21 }, { 22 }, { 23 }

code no      25:
================
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0
1 0 0 0 1 1 1 0 1 1 0 0 1 1 0 0 0 0 0 1 0 0 0
0 1 1 0 1 1 0 1 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0
0 1 0 0 1 0 0 1 1 1 0 1 0 1 1 0 0 0 0 0 0 1 0
0 1 0 1 1 0 1 0 1 1 1 0 1 0 0 1 0 0 0 0 0 0 1
the automorphism group has order 4
and is strongly generated by the following 2 elements:
(
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
, 
0 1 0 0 1 0 0 1 1 1 0 1 0 1 1 0 
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 
1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 
1 0 0 0 1 1 1 0 1 1 0 0 1 1 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 
0 1 1 0 1 1 0 1 1 0 1 0 1 0 1 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 
)
acting on the columns of the generator matrix as follows (in order):
(2, 5)(3, 6)(4, 7)(11, 13)(12, 14)(19, 20), 
(1, 22)(2, 4, 5, 7)(3, 20, 6, 19)(8, 21)(9, 15)(10, 18)(11, 12, 13, 14)(16, 17)
orbits: { 1, 22 }, { 2, 5, 7, 4 }, { 3, 6, 19, 20 }, { 8, 21 }, { 9, 15 }, { 10, 18 }, { 11, 13, 14, 12 }, { 16, 17 }, { 23 }

code no      26:
================
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0
1 0 0 0 1 1 1 0 1 1 0 0 1 1 0 0 0 0 0 1 0 0 0
0 1 1 0 1 1 0 1 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0
0 1 0 0 1 0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0
0 0 0 1 1 0 0 1 1 1 1 0 1 0 0 1 0 0 0 0 0 0 1
the automorphism group has order 4
and is strongly generated by the following 2 elements:
(
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 
0 0 0 1 1 0 0 1 1 1 1 0 1 0 0 1 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 
1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
1 0 0 0 1 1 1 0 1 1 0 0 1 1 0 0 
0 1 1 0 1 1 0 1 1 0 1 0 1 0 1 0 
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 
, 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 
0 1 0 0 1 0 1 0 1 0 1 1 0 1 1 0 
1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 
0 1 1 0 1 1 0 1 1 0 1 0 1 0 1 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 
1 0 0 0 1 1 1 0 1 1 0 0 1 1 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(1, 13)(2, 23)(3, 16)(6, 10)(7, 9)(11, 18)(12, 19)(14, 20)(15, 21)(17, 22), 
(1, 21, 13, 15)(2, 11, 23, 18)(3, 20, 16, 14)(4, 8)(6, 19, 10, 12)(7, 22, 9, 17)
orbits: { 1, 13, 15, 21 }, { 2, 23, 18, 11 }, { 3, 16, 14, 20 }, { 4, 8 }, { 5 }, { 6, 10, 12, 19 }, { 7, 9, 17, 22 }

code no      27:
================
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 0 0 0 0
1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 1 0 0 0 0
1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 1 0 0 0
1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 0 0 0 0 1 0 0
0 1 0 1 1 0 0 1 0 0 0 1 0 1 1 1 0 0 0 0 0 1 0
0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1
the automorphism group has order 20
and is strongly generated by the following 3 elements:
(
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 
, 
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 
1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 
1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 
1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 
, 
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 
1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 
1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(3, 6)(4, 5)(9, 10)(11, 13)(12, 14)(15, 16)(18, 19)(20, 21), 
(2, 6)(3, 13)(4, 10)(7, 9)(8, 19)(12, 21)(14, 17)(16, 18), 
(2, 4, 11, 9)(3, 10)(5, 6, 7, 13)(8, 16, 15, 19)(14, 17, 21, 20)(22, 23)
orbits: { 1 }, { 2, 6, 9, 3, 5, 10, 7, 11, 13, 4 }, { 8, 19, 18, 15, 16 }, { 12, 14, 21, 17, 20 }, { 22, 23 }

code no      28:
================
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 0 0 0 0
1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 1 0 0 0 0
1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 1 0 0 0
0 0 1 1 0 1 0 1 1 0 0 1 1 0 0 1 0 0 0 0 1 0 0
0 1 0 1 0 1 0 1 0 1 0 0 0 1 1 1 0 0 0 0 0 1 0
1 1 1 1 0 1 1 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1
the automorphism group has order 24
and is strongly generated by the following 4 elements:
(
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 
1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 
1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 
1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 
0 1 0 1 0 1 0 1 0 1 0 0 0 1 1 1 
, 
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 
1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
0 0 1 1 0 1 0 1 1 0 0 1 1 0 0 1 
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 1 0 1 0 1 0 1 0 1 0 0 0 1 1 1 
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 
, 
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 
1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 
1 1 1 1 0 1 1 0 0 0 1 1 1 1 1 1 
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 
1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 
0 1 0 1 0 1 0 1 0 1 0 0 0 1 1 1 
, 
1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 
0 1 0 1 0 1 0 1 0 1 0 0 0 1 1 1 
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 
1 1 1 1 0 1 1 0 0 0 1 1 1 1 1 1 
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 
1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 
0 0 1 1 0 1 0 1 1 0 0 1 1 0 0 1 
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(2, 3)(6, 7)(10, 11)(12, 18)(14, 20)(15, 19)(16, 22)(21, 23), 
(1, 14)(2, 19)(3, 16)(4, 21)(5, 10)(7, 17)(8, 12)(15, 22), 
(1, 5)(2, 3)(4, 8)(6, 7)(9, 13)(10, 20)(11, 14)(12, 23)(15, 19)(16, 22)(18, 21), 
(1, 18)(2, 15)(3, 22)(4, 11)(5, 23)(6, 17)(8, 20)(9, 13)(10, 21)(12, 14)
orbits: { 1, 14, 5, 18, 20, 11, 12, 10, 23, 21, 8, 4 }, { 2, 3, 19, 15, 16, 22 }, { 6, 7, 17 }, { 9, 13 }

code no      29:
================
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 0 0 0 0
1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 1 0 0 0 0
1 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 1 0 0 0
0 0 1 1 0 1 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 0 0
1 0 0 0 0 1 1 0 1 0 1 1 0 0 1 1 0 0 0 0 0 1 0
0 1 1 0 0 0 0 1 0 1 0 0 1 1 1 1 0 0 0 0 0 0 1
the automorphism group has order 120
and is strongly generated by the following 5 elements:
(
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 
1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 
1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 
0 1 1 0 0 0 0 1 0 1 0 0 1 1 1 1 
, 
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
1 0 0 0 0 1 1 0 1 0 1 1 0 0 1 1 
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 
1 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 
0 0 1 1 0 1 0 1 1 0 0 1 0 1 0 1 
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 
, 
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 1 1 0 0 0 0 1 0 1 0 0 1 1 1 1 
0 0 1 1 0 1 0 1 1 0 0 1 0 1 0 1 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 
1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 
1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 
1 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
, 
1 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 
1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
, 
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 
1 0 0 0 0 1 1 0 1 0 1 1 0 0 1 1 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 
1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 
0 1 1 0 0 0 0 1 0 1 0 0 1 1 1 1 
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(3, 9)(4, 10)(7, 13)(8, 19)(12, 18)(14, 17)(16, 23)(21, 22), 
(2, 8)(3, 17)(4, 5)(9, 22)(11, 16)(12, 15)(13, 20)(14, 21), 
(2, 16, 19, 11, 8, 23)(3, 17, 14, 9, 22, 21)(4, 18, 5, 12, 10, 15)(7, 20, 13), 
(1, 20)(2, 15)(3, 7)(4, 10)(5, 11)(8, 19)(9, 13)(14, 17), 
(1, 9, 21, 17)(2, 5)(3, 13, 20, 22)(4, 19, 23, 15)(7, 14)(8, 10, 18, 11)(12, 16)
orbits: { 1, 20, 17, 13, 7, 14, 3, 21, 9, 22 }, { 2, 8, 23, 15, 5, 19, 11, 16, 12, 10, 4, 18 }, { 6 }