the 20 isometry classes of irreducible [19,14,4]_3 codes are:

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

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

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

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

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

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

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

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

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

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

code no      11:
================
1 1 1 1 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 1 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 1 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0
1 0 1 1 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 0
2 0 1 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 0
0 2 1 0 1 0 0 0 0 0 0 0 2 0 0 0 0 0 0
2 0 0 1 1 0 0 0 0 0 0 0 0 2 0 0 0 0 0
0 2 0 1 1 0 0 0 0 0 0 0 0 0 2 0 0 0 0
1 0 2 1 1 0 0 0 0 0 0 0 0 0 0 2 0 0 0
0 1 2 1 1 0 0 0 0 0 0 0 0 0 0 0 2 0 0
1 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 2 0
0 1 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 2
the automorphism group has order 72
and is strongly generated by the following 5 elements:
(
2 0 0 0 0 
0 2 0 0 0 
0 0 0 2 0 
0 0 2 0 0 
0 0 0 0 2 
, 
1 0 0 0 0 
1 1 1 1 1 
1 0 2 1 1 
1 0 1 2 1 
2 0 2 2 0 
, 
2 0 1 0 1 
0 2 1 0 1 
0 0 0 0 1 
0 0 0 2 0 
0 0 1 0 0 
, 
2 2 2 0 0 
2 0 0 1 1 
2 0 1 2 2 
2 0 2 2 0 
1 0 1 2 1 
, 
0 1 1 2 1 
0 1 1 1 0 
1 1 0 1 0 
0 1 2 0 2 
2 0 1 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(3, 4)(7, 8)(12, 14)(13, 15)(16, 18)(17, 19), 
(2, 6)(3, 16)(4, 18)(5, 9)(7, 15)(8, 13), 
(1, 12)(2, 13)(3, 5)(6, 8)(9, 16)(10, 17), 
(1, 15, 6, 14, 2, 7)(3, 17, 16)(4, 10, 18, 5, 19, 9)(8, 12, 13), 
(1, 9, 15, 19)(2, 18, 14, 10)(3, 8)(4, 12, 5, 13)(6, 16, 7, 17)
orbits: { 1, 12, 7, 19, 14, 8, 4, 15, 2, 16, 17, 5, 6, 18, 13, 3, 9, 10 }, { 11 }

code no      12:
================
1 1 1 1 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 1 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 1 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0
1 0 1 1 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 0
2 0 1 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 0
2 1 2 0 1 0 0 0 0 0 0 0 2 0 0 0 0 0 0
1 2 2 0 1 0 0 0 0 0 0 0 0 2 0 0 0 0 0
0 2 0 1 1 0 0 0 0 0 0 0 0 0 2 0 0 0 0
1 0 2 1 1 0 0 0 0 0 0 0 0 0 0 2 0 0 0
2 1 0 2 1 0 0 0 0 0 0 0 0 0 0 0 2 0 0
1 2 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 2 0
0 1 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 2
the automorphism group has order 72
and is strongly generated by the following 3 elements:
(
1 0 0 0 0 
1 1 0 1 0 
0 0 0 0 2 
2 0 1 0 1 
0 1 0 2 2 
, 
0 1 0 0 0 
2 1 0 1 2 
0 1 1 1 0 
2 1 0 2 1 
0 0 0 2 0 
, 
0 1 0 2 2 
1 2 0 1 2 
2 2 2 2 2 
2 0 0 0 0 
0 1 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(2, 13, 6, 8)(3, 9, 15, 5)(4, 14, 17, 12)(7, 19, 16, 18), 
(1, 8, 18, 2)(3, 12, 9, 10)(4, 5, 15, 17)(6, 13, 16, 7), 
(1, 4, 18, 15)(2, 5, 8, 17)(3, 16, 9, 6)(7, 12, 13, 10)(14, 19)
orbits: { 1, 2, 15, 8, 18, 17, 9, 5, 6, 16, 4, 14, 3, 12, 13, 7, 19, 10 }, { 11 }

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

code no      14:
================
1 1 1 1 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 1 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 1 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0
1 0 1 1 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0
2 1 0 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 0
2 0 1 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 0
1 2 1 0 1 0 0 0 0 0 0 0 2 0 0 0 0 0 0
1 1 2 0 1 0 0 0 0 0 0 0 0 2 0 0 0 0 0
0 2 2 0 1 0 0 0 0 0 0 0 0 0 2 0 0 0 0
0 2 1 1 1 0 0 0 0 0 0 0 0 0 0 2 0 0 0
0 1 2 1 1 0 0 0 0 0 0 0 0 0 0 0 2 0 0
0 1 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 2 0
0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 2
the automorphism group has order 36
and is strongly generated by the following 5 elements:
(
2 0 0 0 0 
2 1 2 0 2 
2 2 1 0 2 
2 2 2 2 2 
1 1 1 0 0 
, 
2 0 0 0 0 
2 2 1 0 2 
2 1 2 0 2 
2 2 2 2 2 
1 1 1 0 0 
, 
2 0 2 2 0 
0 2 2 2 0 
0 2 1 2 2 
0 1 0 2 1 
0 2 1 1 1 
, 
1 1 1 1 1 
0 2 1 1 1 
0 1 2 1 1 
0 0 0 1 0 
0 2 2 2 0 
, 
0 0 1 2 1 
0 2 2 2 0 
0 1 2 2 2 
2 2 0 2 0 
0 1 2 1 1 
)
acting on the columns of the generator matrix as follows (in order):
(2, 13)(3, 14)(4, 6)(5, 7)(8, 19)(9, 18), 
(2, 14)(3, 13)(4, 6)(5, 7)(8, 18)(9, 19)(11, 12)(16, 17), 
(1, 9)(2, 10)(3, 17)(4, 18)(5, 16)(6, 11)(7, 13)(8, 12), 
(1, 6)(2, 16)(3, 17)(5, 10)(8, 12)(9, 11), 
(1, 9, 19)(2, 14, 10)(3, 7, 16)(4, 11, 8)(5, 13, 17)(6, 18, 12)
orbits: { 1, 9, 6, 19, 18, 11, 4, 12, 8 }, { 2, 13, 14, 10, 16, 3, 7, 5, 17 }, { 15 }

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

code no      16:
================
1 1 1 1 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 1 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 1 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0
1 0 1 1 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0
2 1 0 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 0
1 2 1 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 0
0 2 2 0 1 0 0 0 0 0 0 0 2 0 0 0 0 0 0
2 2 0 1 1 0 0 0 0 0 0 0 0 2 0 0 0 0 0
2 0 2 1 1 0 0 0 0 0 0 0 0 0 2 0 0 0 0
0 1 2 1 1 0 0 0 0 0 0 0 0 0 0 2 0 0 0
1 2 0 2 1 0 0 0 0 0 0 0 0 0 0 0 2 0 0
0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 2 0
2 1 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 2
the automorphism group has order 36
and is strongly generated by the following 3 elements:
(
1 0 0 0 0 
1 1 1 1 1 
0 0 1 2 1 
2 0 2 1 1 
2 0 2 2 0 
, 
0 1 2 1 1 
1 0 1 2 2 
2 2 2 0 0 
2 2 0 2 0 
0 0 1 2 1 
, 
2 0 2 1 1 
1 2 2 1 2 
1 2 0 2 1 
0 0 0 0 2 
0 2 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(2, 6)(3, 18)(4, 15)(5, 9)(7, 12)(8, 14)(13, 17)(16, 19), 
(1, 16)(2, 15)(3, 7)(4, 8)(5, 18)(6, 14)(9, 12)(10, 17), 
(1, 17, 3, 15)(2, 5, 4, 19)(6, 7, 13, 9)(8, 12, 10, 16)(14, 18)
orbits: { 1, 16, 15, 19, 10, 4, 2, 3, 17, 12, 8, 5, 6, 18, 7, 13, 9, 14 }, { 11 }

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

code no      18:
================
1 1 1 1 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 1 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 1 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0
1 0 1 1 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0
2 1 1 1 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 0
2 0 1 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 0
0 2 1 0 1 0 0 0 0 0 0 0 2 0 0 0 0 0 0
2 1 2 0 1 0 0 0 0 0 0 0 0 2 0 0 0 0 0
1 2 2 0 1 0 0 0 0 0 0 0 0 0 2 0 0 0 0
2 0 0 1 1 0 0 0 0 0 0 0 0 0 0 2 0 0 0
2 2 1 1 1 0 0 0 0 0 0 0 0 0 0 0 2 0 0
1 0 2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 2 0
1 2 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 2
the automorphism group has order 288
and is strongly generated by the following 6 elements:
(
1 0 0 0 0 
0 1 0 0 0 
2 2 0 0 2 
1 1 1 1 1 
2 2 2 0 0 
, 
1 0 0 0 0 
0 0 1 0 0 
0 1 0 0 0 
0 0 0 1 0 
0 2 1 0 1 
, 
2 0 0 0 0 
2 2 2 0 0 
0 2 1 0 1 
1 1 2 2 2 
2 1 1 0 2 
, 
2 2 2 0 0 
0 1 0 0 0 
0 0 1 0 0 
2 1 1 1 0 
1 2 2 0 1 
, 
2 2 0 0 2 
1 2 2 0 1 
0 2 1 0 1 
2 2 2 2 2 
0 0 1 0 0 
, 
1 1 0 1 0 
1 2 2 2 0 
0 0 0 2 0 
0 2 0 0 0 
2 0 0 1 1 
)
acting on the columns of the generator matrix as follows (in order):
(3, 11)(4, 6)(5, 7)(8, 17)(12, 13)(18, 19), 
(2, 3)(5, 13)(6, 18)(8, 9)(11, 15)(16, 17), 
(2, 13, 3, 12, 15, 5, 11, 7)(4, 9, 18, 8, 19, 16, 6, 17), 
(1, 7)(4, 10)(5, 15)(6, 16)(11, 13)(17, 18), 
(1, 13, 3, 5, 7, 15, 2, 11)(4, 16, 9, 17, 10, 18, 8, 6), 
(1, 9, 7, 8)(2, 4, 3, 10)(5, 18, 11, 16)(6, 13, 17, 15)(12, 19)
orbits: { 1, 7, 11, 8, 5, 9, 3, 15, 13, 2, 18, 17, 16, 4, 12, 6, 10, 19 }, { 14 }

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

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