the 9 isometry classes of irreducible [23,17,4]_2 codes are:

code no       1:
================
1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
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 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 21504
and is strongly generated by the following 8 elements:
(
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
0 1 0 1 1 0 
0 0 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
1 0 0 1 1 0 
0 0 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
0 0 1 1 1 0 
0 0 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 1 0 1 0 0 
1 0 1 0 1 0 
1 1 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 0 1 1 0 0 
1 1 0 0 1 0 
1 0 1 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
1 0 1 1 0 0 
1 1 0 1 0 0 
1 1 0 0 1 0 
0 1 0 1 0 1 
, 
1 0 0 0 0 0 
1 1 0 1 0 0 
0 1 1 1 0 0 
1 1 1 0 0 0 
1 0 0 1 1 0 
0 0 1 1 0 1 
, 
0 1 0 1 1 0 
1 0 0 1 1 0 
1 1 1 1 1 0 
1 0 1 0 1 0 
0 1 0 0 0 0 
0 1 1 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(5, 15)(11, 14)(12, 17)(13, 16), 
(5, 14)(11, 15)(12, 16)(13, 17), 
(5, 16)(11, 17)(12, 14)(13, 15), 
(4, 8)(5, 12)(6, 18)(9, 10)(11, 13)(14, 17)(15, 16)(19, 20), 
(4, 9)(5, 11)(6, 19)(8, 10)(12, 13)(14, 17)(15, 16)(18, 20), 
(3, 10, 7, 9)(4, 8)(5, 11)(6, 21, 18, 22)(12, 16, 13, 17)(19, 20), 
(2, 10, 3, 7, 4, 9, 8)(5, 16, 13, 12, 15, 17, 14)(6, 22, 21, 20, 18, 19, 23), 
(1, 11, 10, 15)(2, 5, 9, 14)(3, 13, 8, 17)(4, 16, 7, 12)(6, 20)(18, 19)
orbits: { 1, 15, 5, 11, 13, 16, 12, 10, 14, 2, 17, 3, 4, 7, 9, 8 }, { 6, 18, 19, 22, 23, 20, 21 }

code no       2:
================
1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 768
and is strongly generated by the following 6 elements:
(
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
1 1 0 0 1 0 
1 1 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 1 0 1 0 0 
1 1 0 0 1 0 
1 1 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 0 1 1 0 0 
0 1 1 0 1 0 
0 1 1 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
1 0 1 1 0 0 
1 1 0 1 0 0 
0 1 0 1 1 0 
0 1 0 1 0 1 
, 
0 0 0 1 0 0 
1 1 0 1 0 0 
1 0 1 1 0 0 
1 1 1 0 0 0 
1 1 1 1 1 0 
0 1 1 0 0 1 
, 
0 0 1 1 1 0 
1 1 1 1 1 0 
1 0 0 1 1 0 
0 0 0 0 1 0 
0 0 0 1 0 0 
1 0 1 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(5, 11)(6, 18)(12, 13)(14, 15)(16, 17)(19, 20)(21, 22), 
(4, 8)(5, 11)(6, 18)(9, 10)(12, 13)(19, 20), 
(4, 9)(5, 13)(6, 20)(8, 10)(11, 12)(14, 15)(16, 17)(18, 19)(21, 22), 
(3, 10, 7, 9)(4, 8)(5, 14, 11, 15)(6, 21, 18, 22)(12, 13)(19, 20), 
(1, 10, 7, 4)(2, 9, 3, 8)(5, 14, 13, 17)(6, 20)(11, 15, 12, 16)(18, 19), 
(1, 16)(2, 17)(3, 14)(4, 5)(6, 19)(7, 15)(8, 11)(9, 12)(10, 13)(18, 20)
orbits: { 1, 4, 16, 8, 9, 7, 5, 17, 12, 10, 3, 11, 2, 15, 13, 14 }, { 6, 18, 20, 22, 19, 21 }, { 23 }

code no       3:
================
1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 1152
and is strongly generated by the following 8 elements:
(
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
1 0 0 1 1 0 
0 0 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 0 1 0 
0 0 0 1 0 0 
0 0 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 0 0 1 1 0 
0 0 0 1 0 0 
0 0 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
1 1 1 0 0 0 
0 0 0 1 0 0 
0 0 0 0 1 0 
0 0 0 0 0 1 
, 
1 0 0 0 0 0 
1 1 1 0 0 0 
0 1 0 0 0 0 
0 0 0 0 1 0 
0 0 0 1 0 0 
0 0 0 0 0 1 
, 
1 0 0 0 0 0 
1 0 0 1 1 0 
0 0 0 0 1 0 
1 1 1 0 0 0 
0 0 1 0 0 0 
0 0 0 0 0 1 
, 
0 0 1 1 1 0 
1 0 0 1 1 0 
1 1 1 1 1 0 
1 0 1 0 1 0 
1 0 1 1 0 0 
0 0 0 0 0 1 
, 
0 1 1 0 1 0 
0 0 0 0 1 0 
1 1 0 0 1 0 
1 1 1 1 1 0 
1 1 1 0 0 0 
0 0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(5, 14)(11, 15)(12, 16)(13, 17)(22, 23), 
(4, 5)(8, 11)(9, 12)(10, 13)(21, 22), 
(4, 5, 14)(8, 11, 15)(9, 12, 16)(10, 13, 17)(21, 22, 23), 
(3, 7)(9, 10)(12, 13)(16, 17)(19, 20), 
(2, 3, 7)(4, 5)(8, 12, 10, 11, 9, 13)(15, 16, 17)(18, 19, 20)(21, 22), 
(2, 14)(3, 5)(4, 7)(8, 17)(9, 13)(11, 16)(18, 23)(19, 22)(20, 21), 
(1, 15, 7, 16)(2, 17, 3, 14)(4, 11, 10, 12)(5, 8, 13, 9)(18, 19), 
(1, 11, 3, 13)(2, 12, 7, 5)(4, 15, 9, 17)(8, 16, 10, 14)(18, 20)
orbits: { 1, 16, 13, 12, 17, 15, 11, 7, 8, 10, 9, 3, 2, 4, 5, 14 }, { 6 }, { 18, 20, 23, 19, 21, 22 }

code no       4:
================
1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
0 1 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 336
and is strongly generated by the following 5 elements:
(
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
0 0 0 0 0 1 
0 0 0 0 1 0 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 1 0 1 0 0 
1 1 0 0 1 0 
1 1 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 1 1 1 0 0 
0 1 1 0 1 0 
0 1 1 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
1 1 0 1 0 0 
0 1 1 1 0 0 
1 0 0 1 1 0 
1 0 0 1 0 1 
, 
1 0 0 0 0 0 
1 0 1 1 0 0 
0 0 1 0 0 0 
1 1 1 0 0 0 
0 0 0 0 1 0 
0 0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(5, 6)(11, 17)(12, 18)(13, 19)(14, 20)(15, 21)(16, 22), 
(4, 8)(5, 11)(6, 17)(9, 10)(12, 13)(18, 19), 
(4, 10)(5, 13)(6, 19)(8, 9)(11, 12)(17, 18), 
(3, 9, 8)(4, 7, 10)(5, 13, 14)(6, 19, 20)(11, 12, 15)(17, 18, 21), 
(2, 9)(4, 7)(11, 16)(13, 14)(17, 22)(19, 20)
orbits: { 1 }, { 2, 9, 10, 8, 3, 4, 7 }, { 5, 6, 11, 13, 14, 17, 19, 20, 12, 15, 16, 18, 21, 22 }, { 23 }

code no       5:
================
1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 384
and is strongly generated by the following 7 elements:
(
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
0 0 0 0 1 0 
1 1 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 1 0 1 0 0 
1 1 0 0 1 0 
1 1 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 1 1 1 0 0 
0 1 1 0 1 0 
0 1 1 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 1 0 0 1 0 
1 1 0 1 0 0 
1 1 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
1 1 0 1 0 0 
0 0 1 0 0 0 
1 1 0 0 1 0 
1 1 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
1 1 0 0 1 0 
1 0 1 0 1 0 
0 1 0 1 1 0 
0 1 0 0 1 1 
, 
0 1 0 0 0 0 
1 0 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
0 0 0 0 1 0 
1 1 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(6, 17)(18, 19)(20, 21)(22, 23), 
(4, 8)(5, 11)(6, 17)(9, 10)(12, 13)(18, 19), 
(4, 10)(5, 13)(6, 19)(8, 9)(11, 12)(17, 18), 
(4, 11)(5, 8)(6, 17)(9, 13)(10, 12)(18, 19)(20, 22)(21, 23), 
(3, 4, 7, 8)(5, 11)(6, 17)(9, 10)(12, 15, 13, 14)(18, 21, 19, 20), 
(3, 10, 14, 11)(4, 12)(5, 7, 9, 15)(6, 18, 21, 23)(8, 13)(17, 19, 20, 22), 
(1, 2)(6, 17)(9, 10)(12, 13)(14, 15)
orbits: { 1, 2 }, { 3, 8, 11, 4, 9, 5, 7, 13, 12, 14, 10, 15 }, { 6, 17, 19, 23, 18, 22, 21, 20 }, { 16 }

code no       6:
================
1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 32
and is strongly generated by the following 5 elements:
(
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 1 0 1 0 0 
1 1 0 0 1 0 
1 1 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 1 1 1 0 0 
0 1 1 0 1 0 
0 1 1 0 0 1 
, 
1 0 0 0 0 0 
0 0 1 0 0 0 
0 1 0 0 0 0 
1 0 1 0 1 0 
1 0 1 1 0 0 
1 0 1 0 0 1 
, 
0 1 0 0 0 0 
1 0 0 0 0 0 
1 1 1 0 0 0 
0 0 0 1 0 0 
1 1 0 0 1 0 
0 0 0 0 0 1 
, 
1 1 1 0 0 0 
0 0 1 0 0 0 
0 1 0 0 0 0 
1 0 1 1 0 0 
1 1 0 0 1 0 
0 0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(4, 8)(5, 11)(6, 17)(9, 10)(12, 13)(18, 19), 
(4, 10)(5, 13)(6, 19)(8, 9)(11, 12)(17, 18), 
(2, 3)(4, 11, 10, 12)(5, 8, 13, 9)(6, 17, 19, 18)(15, 16)(20, 22)(21, 23), 
(1, 2)(3, 7)(5, 11)(12, 13)(20, 21), 
(1, 7)(2, 3)(4, 9)(5, 11)(8, 10)(12, 13)(20, 21)(22, 23)
orbits: { 1, 2, 7, 3 }, { 4, 8, 10, 12, 9, 5, 11, 13 }, { 6, 17, 19, 18 }, { 14 }, { 15, 16 }, { 20, 22, 21, 23 }

code no       7:
================
1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 48
and is strongly generated by the following 6 elements:
(
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
1 1 0 0 1 0 
1 1 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
1 1 0 0 0 1 
1 1 0 0 1 0 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 0 1 0 0 
0 0 1 0 0 0 
1 1 0 0 1 0 
1 1 0 0 0 1 
, 
0 1 0 0 0 0 
1 0 0 0 0 0 
1 1 1 0 0 0 
1 1 0 1 0 0 
1 1 0 0 1 0 
0 0 0 0 0 1 
, 
1 1 1 0 0 0 
0 0 1 0 0 0 
0 1 0 0 0 0 
1 1 0 1 0 0 
0 1 1 0 1 0 
1 0 1 0 0 1 
, 
1 1 0 1 0 0 
0 0 0 1 0 0 
0 1 0 0 0 0 
1 1 1 0 0 0 
0 1 0 1 1 0 
1 0 0 1 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(5, 11)(6, 16)(12, 13)(14, 15)(17, 18)(19, 20), 
(5, 16)(6, 11)(12, 18)(13, 17)(14, 20)(15, 19), 
(3, 4)(5, 11)(6, 16)(7, 8)(12, 15)(13, 14)(17, 20)(18, 19)(22, 23), 
(1, 2)(3, 7)(4, 8)(5, 11)(9, 10)(12, 13)(14, 15), 
(1, 7)(2, 3)(4, 8)(5, 13)(6, 17)(9, 10)(11, 12)(14, 15)(16, 18)(21, 22), 
(1, 7, 4, 2, 3, 8)(5, 13, 14, 11, 12, 15)(6, 17, 19)(9, 10)(16, 18, 20)(21, 22, 23)
orbits: { 1, 2, 7, 8, 3, 4 }, { 5, 11, 16, 13, 15, 6, 12, 14, 18, 20, 17, 19 }, { 9, 10 }, { 21, 22, 23 }

code no       8:
================
1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
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 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 48
and is strongly generated by the following 4 elements:
(
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 1 1 1 0 0 
1 0 1 0 1 0 
1 1 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
1 1 1 0 0 0 
0 0 0 0 1 0 
0 0 0 1 0 0 
0 0 0 0 0 1 
, 
1 0 0 0 0 0 
1 1 1 0 0 0 
0 0 1 0 0 0 
1 1 0 0 0 1 
1 0 1 0 1 0 
0 1 1 1 0 0 
, 
0 0 1 0 0 0 
1 1 1 0 0 0 
1 0 0 0 0 0 
1 0 1 1 0 0 
0 0 0 0 1 0 
1 0 1 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(4, 10)(5, 12)(6, 16)(8, 9)(11, 13)(14, 15)(17, 18)(19, 20)(21, 22), 
(3, 7)(4, 5)(8, 11)(9, 13)(10, 12)(17, 18)(19, 21)(20, 22), 
(2, 7)(4, 16)(5, 12)(6, 10)(8, 17)(9, 18)(14, 22)(15, 21)(19, 20), 
(1, 3)(2, 7)(4, 9)(6, 17)(8, 10)(16, 18)(19, 20)
orbits: { 1, 3, 7, 2 }, { 4, 10, 5, 16, 9, 12, 6, 8, 18, 13, 17, 11 }, { 14, 15, 22, 21, 20, 19 }, { 23 }

code no       9:
================
1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
1 0 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 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1
the automorphism group has order 144
and is strongly generated by the following 5 elements:
(
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 0 1 1 0 0 
1 0 1 0 1 0 
0 0 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 0 1 0 1 0 
1 0 1 1 0 0 
0 0 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
1 0 1 0 1 0 
0 0 1 0 0 0 
1 0 1 1 0 0 
0 0 0 0 0 1 
, 
1 0 0 0 0 0 
0 0 0 0 0 1 
0 0 0 1 0 0 
0 0 1 0 0 0 
0 0 0 0 1 0 
0 1 0 0 0 0 
, 
0 1 0 0 0 0 
1 0 0 0 0 0 
1 1 1 0 0 0 
1 1 0 1 0 0 
1 1 0 0 1 0 
0 0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(4, 9)(5, 12)(8, 10)(11, 13)(18, 19)(20, 21), 
(4, 12)(5, 9)(8, 13)(10, 11)(18, 21)(19, 20), 
(3, 4, 14, 12)(5, 9)(7, 8, 15, 13)(10, 11)(17, 18, 22, 21)(19, 20), 
(2, 6)(3, 4)(7, 18)(8, 17)(10, 19)(11, 20)(12, 14)(13, 22)(15, 21), 
(1, 2)(3, 7)(4, 8)(5, 11)(9, 10)(12, 13)(14, 15)
orbits: { 1, 2, 6 }, { 3, 12, 4, 7, 5, 14, 13, 9, 8, 18, 11, 15, 22, 10, 17, 19, 21, 20 }, { 16 }, { 23 }