the 7 isometry classes of irreducible [13,3,8]_3 codes are:

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

code no       2:
================
1 1 1 1 1 1 1 1 1 1 2 0 0
2 2 2 1 1 1 1 0 0 0 0 2 0
2 2 0 2 2 1 0 1 1 0 0 0 2
the automorphism group has order 64
and is strongly generated by the following 6 elements:
(
1 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 1 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 1 0 0 0 
0 0 0 0 0 0 0 1 0 0 
0 0 0 0 0 0 0 0 1 0 
2 2 2 2 2 2 2 2 2 2 
, 
2 0 0 0 0 0 0 0 0 0 
0 2 0 0 0 0 0 0 0 0 
0 0 2 0 0 0 0 0 0 0 
0 0 0 2 0 0 0 0 0 0 
0 0 0 0 2 0 0 0 0 0 
0 0 0 0 0 2 0 0 0 0 
0 0 0 0 0 0 2 0 0 0 
0 0 0 0 0 0 0 0 2 0 
0 0 0 0 0 0 0 2 0 0 
0 0 0 0 0 0 0 0 0 2 
, 
1 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 1 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 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 1 
, 
2 0 0 0 0 0 0 0 0 0 
0 2 0 0 0 0 0 0 0 0 
1 1 0 1 1 2 0 2 2 0 
0 0 0 0 0 0 0 0 0 1 
2 2 2 2 2 2 2 2 2 2 
1 1 1 2 2 2 2 0 0 0 
0 0 0 0 0 0 2 0 0 0 
0 0 0 0 0 0 0 0 2 0 
0 0 0 0 0 0 0 2 0 0 
0 0 0 0 1 0 0 0 0 0 
, 
0 2 0 0 0 0 0 0 0 0 
2 0 0 0 0 0 0 0 0 0 
0 0 2 0 0 0 0 0 0 0 
0 0 0 0 2 0 0 0 0 0 
0 0 0 2 0 0 0 0 0 0 
0 0 0 0 0 2 0 0 0 0 
0 0 0 0 0 0 2 0 0 0 
0 0 0 0 0 0 0 0 2 0 
0 0 0 0 0 0 0 2 0 0 
1 1 1 1 1 1 1 1 1 1 
, 
0 0 0 0 0 0 0 0 2 0 
0 0 0 0 0 0 0 2 0 0 
0 0 0 0 0 2 0 0 0 0 
0 0 0 0 0 0 0 0 0 2 
1 1 1 1 1 1 1 1 1 1 
0 0 2 0 0 0 0 0 0 0 
0 0 0 0 0 0 2 0 0 0 
0 2 0 0 0 0 0 0 0 0 
2 0 0 0 0 0 0 0 0 0 
0 0 0 2 0 0 0 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(10, 11), 
(8, 9), 
(4, 5)(8, 9), 
(3, 13)(4, 11, 5, 10)(6, 12)(8, 9), 
(1, 2)(4, 5)(8, 9)(10, 11), 
(1, 9)(2, 8)(3, 6)(4, 10)(5, 11)(12, 13)
orbits: { 1, 2, 9, 8 }, { 3, 13, 6, 12 }, { 4, 5, 10, 11 }, { 7 }

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

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

code no       5:
================
1 1 1 1 1 1 1 0 0 0 2 0 0
2 2 1 1 1 0 0 1 1 0 0 2 0
2 1 2 2 0 1 0 1 0 1 0 0 2
the automorphism group has order 128
and is strongly generated by the following 7 elements:
(
2 0 0 0 0 0 0 0 0 0 
0 2 0 0 0 0 0 0 0 0 
0 0 2 0 0 0 0 0 0 0 
0 0 0 2 0 0 0 0 0 0 
0 0 0 0 2 0 0 0 0 0 
0 0 0 0 0 2 0 0 0 0 
0 0 0 0 0 0 2 0 0 0 
0 0 0 0 0 0 0 2 0 0 
0 0 0 0 0 0 0 0 2 0 
2 1 2 2 0 1 0 1 0 1 
, 
2 0 0 0 0 0 0 0 0 0 
0 2 0 0 0 0 0 0 0 0 
0 0 2 0 0 0 0 0 0 0 
0 0 0 2 0 0 0 0 0 0 
0 0 0 0 2 0 0 0 0 0 
0 0 0 0 0 2 0 0 0 0 
0 0 0 0 0 0 2 0 0 0 
0 0 0 0 0 0 0 2 0 0 
2 2 1 1 1 0 0 1 1 0 
0 0 0 0 0 0 0 0 0 2 
, 
1 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 1 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 
2 2 2 2 2 2 2 0 0 0 
0 0 0 0 0 0 0 1 0 0 
1 1 2 2 2 0 0 2 2 0 
0 0 0 0 0 0 0 0 0 1 
, 
1 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 1 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 
2 2 2 2 2 2 2 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 1 
, 
2 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 1 0 0 
2 2 1 1 1 0 0 1 1 0 
0 0 0 0 0 0 0 0 2 0 
0 0 0 0 2 0 0 0 0 0 
0 0 0 0 0 2 0 0 0 0 
0 0 0 0 0 0 0 0 0 2 
0 1 0 0 0 0 0 0 0 0 
0 0 2 0 0 0 0 0 0 0 
1 1 1 1 1 1 1 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 2 0 0 0 0 0 0 0 
0 0 0 2 0 0 0 0 0 0 
0 0 0 0 2 0 0 0 0 0 
0 0 0 0 0 0 0 2 0 0 
2 2 1 1 1 0 0 1 1 0 
0 0 0 0 0 2 0 0 0 0 
0 0 0 0 0 0 2 0 0 0 
0 0 0 0 0 0 0 0 0 2 
, 
0 0 0 0 0 1 0 0 0 0 
0 0 0 0 0 0 0 2 0 0 
1 2 1 1 0 2 0 2 0 2 
0 0 0 0 0 0 0 0 0 1 
0 0 0 0 1 0 0 0 0 0 
1 0 0 0 0 0 0 0 0 0 
1 1 2 2 2 0 0 2 2 0 
0 2 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 
)
acting on the columns of the generator matrix as follows (in order):
(10, 13), 
(9, 12), 
(7, 11)(9, 12), 
(3, 4)(7, 11), 
(2, 8)(3, 9, 4, 12)(7, 13, 11, 10), 
(1, 2)(6, 8)(7, 9, 11, 12), 
(1, 6)(2, 8)(3, 13)(4, 10)(7, 9, 11, 12)
orbits: { 1, 2, 6, 8 }, { 3, 4, 12, 13, 9, 10, 11, 7 }, { 5 }

code no       6:
================
1 1 1 1 1 1 1 0 0 0 2 0 0
2 2 1 1 1 0 0 1 1 0 0 2 0
0 0 2 1 0 2 1 2 1 1 0 0 2
the automorphism group has order 288
and is strongly generated by the following 7 elements:
(
1 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 1 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 1 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 1 2 0 1 2 1 2 2 
, 
2 0 0 0 0 0 0 0 0 0 
0 2 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 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 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 
, 
1 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 1 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 
2 2 2 2 2 2 2 0 0 0 
0 0 0 0 0 0 1 0 0 0 
1 1 2 2 2 0 0 2 2 0 
0 0 0 0 0 0 0 0 1 0 
0 0 0 0 0 0 0 0 0 2 
, 
2 0 0 0 0 0 0 0 0 0 
0 2 0 0 0 0 0 0 0 0 
1 1 2 2 2 0 0 2 2 0 
0 0 0 0 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 
0 0 0 0 1 0 0 0 0 0 
0 0 0 0 0 0 2 0 0 0 
1 1 1 1 1 1 1 0 0 0 
0 0 0 0 0 0 0 0 0 2 
, 
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 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 
2 2 2 2 2 2 2 0 0 0 
0 0 0 0 0 0 0 0 1 0 
1 1 2 2 2 0 0 2 2 0 
0 0 0 0 0 0 0 0 0 1 
, 
0 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 1 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 1 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 2 
, 
0 0 2 1 0 2 1 2 1 1 
0 0 0 0 0 0 0 0 0 2 
0 0 0 1 0 0 0 0 0 0 
0 0 0 0 0 0 0 2 0 0 
0 0 0 0 0 2 0 0 0 0 
1 1 2 2 2 0 0 2 2 0 
0 0 0 0 2 0 0 0 0 0 
0 0 0 0 0 0 0 0 1 0 
0 0 2 0 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):
(10, 13), 
(6, 8)(7, 9)(11, 12), 
(4, 5)(6, 11)(8, 12), 
(3, 6, 12)(4, 11, 9)(5, 7, 8), 
(3, 4, 5)(6, 11, 7)(8, 12, 9), 
(1, 2)(3, 4)(6, 7)(8, 9), 
(1, 13)(2, 10)(3, 9, 8, 4)(5, 7, 12, 6)
orbits: { 1, 2, 13, 10 }, { 3, 12, 5, 4, 11, 8, 6, 7, 9 }

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