the 6 isometry classes of irreducible [12,2,7]_3 codes are:

code no       1:
================
1 1 1 1 1 1 1 1 1 1 2 0
2 1 1 1 1 1 0 0 0 0 0 2
the automorphism group has order 57600
and is strongly generated by the following 10 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 
, 
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 0 1 
0 0 0 0 0 0 0 0 1 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 0 0 2 
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 2 0 0 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 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 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 0 0 0 2 
0 0 0 0 0 0 0 0 2 0 
1 1 1 1 1 1 1 1 1 1 
0 0 0 0 0 0 0 2 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 1 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 
2 2 2 2 2 2 2 2 2 2 
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 
, 
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 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 0 0 0 0 2 0 0 
0 0 0 0 0 0 2 0 0 0 
1 1 1 1 1 1 1 1 1 1 
0 0 0 0 0 0 0 0 0 2 
, 
2 0 0 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 0 
0 0 0 2 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 0 0 0 2 0 
0 0 0 0 0 0 2 0 0 0 
1 1 1 1 1 1 1 1 1 1 
0 0 0 0 0 0 0 0 0 2 
, 
1 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 1 
2 2 2 2 2 2 2 2 2 2 
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 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 
, 
1 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 2 0 0 0 0 
0 0 0 0 2 0 0 0 0 0 
0 2 0 0 0 0 0 0 0 0 
2 2 2 2 2 2 2 2 2 2 
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 
)
acting on the columns of the generator matrix as follows (in order):
(10, 11), 
(9, 10), 
(8, 11, 10), 
(7, 11), 
(5, 6)(7, 11, 9, 8, 10), 
(4, 6, 5)(7, 11)(9, 10), 
(3, 6, 5, 4)(7, 8)(9, 11), 
(2, 5, 3, 6)(7, 8, 11, 9), 
(2, 11, 3, 7, 4, 8, 6, 10)(5, 9), 
(1, 12)(2, 6, 4, 3)(7, 8, 11)(9, 10)
orbits: { 1, 12 }, { 2, 6, 10, 3, 5, 4, 8, 11, 9, 7 }

code no       2:
================
1 1 1 1 1 1 1 1 1 1 2 0
2 2 1 1 1 1 0 0 0 0 0 2
the automorphism group has order 5760
and is strongly generated by the following 10 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 
, 
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 0 1 
0 0 0 0 0 0 0 0 1 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 
2 2 2 2 2 2 2 2 2 2 
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 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 0 0 1 
0 0 0 0 0 0 0 0 1 0 
0 0 0 0 0 0 0 1 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 0 0 1 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 
, 
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 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 1 
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 
, 
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 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 
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 2 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 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 
, 
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 0 0 0 1 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 0 0 1 
0 0 0 0 0 0 0 1 0 0 
0 0 0 0 0 0 1 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 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 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 
)
acting on the columns of the generator matrix as follows (in order):
(10, 11), 
(9, 10), 
(9, 11), 
(8, 10), 
(7, 8, 10, 9), 
(5, 6)(7, 9, 10), 
(4, 5, 6)(7, 9, 8, 10), 
(3, 5)(4, 6), 
(3, 5, 6, 4)(7, 10, 8, 9), 
(1, 2)(3, 4, 5, 6)(8, 9)
orbits: { 1, 2 }, { 3, 5, 4, 6 }, { 7, 9, 10, 11, 8 }, { 12 }

code no       3:
================
1 1 1 1 1 1 1 1 1 1 2 0
2 2 2 1 1 1 0 0 0 0 0 2
the automorphism group has order 8640
and is strongly generated by the following 10 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 
, 
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 0 1 
2 2 2 2 2 2 2 2 2 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 
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 
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 
1 1 1 1 1 1 1 1 1 1 
0 0 0 0 0 0 0 2 0 0 
0 0 0 0 0 0 0 0 2 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 0 1 0 0 
0 0 0 0 0 0 0 0 1 0 
0 0 0 0 0 0 1 0 0 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 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 0 0 0 0 2 0 
1 1 1 1 1 1 1 1 1 1 
0 0 0 0 0 0 2 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 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 1 0 
0 0 0 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 0 0 1 
2 2 2 2 2 2 2 2 2 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 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 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 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 0 0 2 0 0 0 0 
0 0 0 2 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 0 2 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 2 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 0 0 0 2 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 2 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(10, 11), 
(9, 11, 10), 
(8, 9)(10, 11), 
(8, 9, 10, 11), 
(7, 9, 8)(10, 11), 
(5, 6)(7, 10, 11, 9, 8), 
(4, 5, 6)(7, 8, 11, 10, 9), 
(2, 3)(7, 10, 9, 8), 
(1, 2)(4, 6, 5)(7, 10, 8, 9, 11), 
(1, 5, 2, 4)(3, 6)(7, 10, 9, 11, 8)
orbits: { 1, 2, 4, 3, 5, 6 }, { 7, 8, 9, 11, 10 }, { 12 }

code no       4:
================
1 1 1 1 1 1 0 0 0 0 2 0
1 1 0 0 0 0 1 1 1 1 0 2
the automorphism group has order 57600
and is strongly generated by the following 12 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 0 0 0 0 1 1 1 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 
0 0 0 0 0 0 0 0 0 1 
0 0 0 0 0 0 0 0 1 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 0 
1 1 0 0 0 0 1 1 1 1 
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 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 0 0 2 
0 0 0 0 0 0 0 2 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 0 2 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 
, 
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 
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 0 2 
0 0 0 0 0 0 0 0 2 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 0 1 0 0 0 0 
2 2 2 2 2 2 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 1 0 0 0 
0 0 0 0 0 0 0 0 1 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 1 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 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 1 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 0 2 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 0 2 0 0 
0 0 0 0 0 0 0 0 0 2 
0 0 0 0 0 0 2 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 
0 0 0 0 0 2 0 0 0 0 
0 0 0 2 0 0 0 0 0 0 
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 0 0 2 
0 0 0 0 0 0 0 0 2 0 
0 0 0 0 0 0 0 2 0 0 
, 
1 0 0 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 0 0 
2 2 0 0 0 0 2 2 2 2 
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 1 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 1 0 0 0 0 0 0 0 
0 0 0 1 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 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 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 0 0 0 0 0 0 2 0 0 
0 0 0 0 0 0 2 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(10, 12), 
(9, 10), 
(9, 12), 
(8, 10, 9), 
(7, 8, 9), 
(6, 11)(9, 10), 
(5, 11, 6)(7, 9, 10, 8), 
(4, 6, 5)(7, 10, 8), 
(3, 4)(5, 6)(7, 10, 9), 
(3, 11, 6, 4, 5)(8, 10), 
(3, 9, 11, 12)(4, 10)(5, 8)(6, 7), 
(1, 2)(3, 6, 5)(7, 10, 8, 9)
orbits: { 1, 2 }, { 3, 4, 5, 12, 6, 10, 8, 9, 11, 7 }

code no       5:
================
1 1 1 1 1 1 0 0 0 0 2 0
1 1 1 0 0 0 1 1 1 1 0 2
the automorphism group has order 17280
and is strongly generated by the following 12 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 0 0 0 2 2 2 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 
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 
, 
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 
1 1 1 0 0 0 1 1 1 1 
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 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 0 2 
0 0 0 0 0 0 0 0 2 0 
0 0 0 0 0 0 0 2 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 
1 1 1 0 0 0 1 1 1 1 
0 0 0 0 0 0 0 0 2 0 
0 0 0 0 0 0 0 2 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 0 2 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 
, 
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 0 0 0 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 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 
2 2 2 2 2 2 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 1 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 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 2 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 
1 1 1 1 1 1 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 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 2 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 
1 1 1 1 1 1 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 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 2 0 
, 
0 0 2 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 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 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 2 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(10, 12), 
(9, 10), 
(9, 12), 
(8, 10), 
(8, 10, 12), 
(7, 8, 9), 
(7, 12)(8, 9), 
(6, 11)(7, 10, 9), 
(5, 6)(7, 10, 8, 9), 
(4, 11)(5, 6)(7, 10, 8, 9), 
(2, 3)(4, 11)(5, 6)(7, 8, 9, 10), 
(1, 3)(4, 5)(7, 9, 8, 10)
orbits: { 1, 3, 2 }, { 4, 11, 5, 6 }, { 7, 9, 12, 10, 8 }

code no       6:
================
1 1 1 1 1 1 0 0 0 0 2 0
2 2 1 1 0 0 1 1 1 1 0 2
the automorphism group has order 5760
and is strongly generated by the following 12 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 2 1 1 0 0 1 1 1 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 
0 0 0 0 0 0 0 0 0 1 
0 0 0 0 0 0 0 0 1 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 0 
2 2 1 1 0 0 1 1 1 1 
0 0 0 0 0 0 0 0 2 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 0 0 2 
0 0 0 0 0 0 0 2 0 0 
0 0 0 0 0 0 0 0 2 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 0 2 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 
, 
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 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 1 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 
2 2 1 1 0 0 1 1 1 1 
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 0 2 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 
2 2 2 2 2 2 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 1 0 0 
0 0 0 0 0 0 1 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 0 0 2 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 
, 
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 
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 0 1 
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 1 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 0 
0 0 0 0 0 0 0 0 1 0 
0 0 0 0 0 0 0 0 0 1 
, 
0 0 0 2 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 
2 0 0 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 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 1 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(10, 12), 
(9, 10), 
(9, 10, 12), 
(8, 9, 10), 
(7, 8, 9), 
(7, 10), 
(7, 9, 10, 8, 12), 
(6, 11)(7, 10, 8, 9), 
(5, 6)(7, 8, 9), 
(5, 11)(7, 10)(8, 9), 
(3, 4), 
(1, 4)(2, 3)(5, 6)(7, 10, 9, 8)
orbits: { 1, 4, 3, 2 }, { 5, 6, 11 }, { 7, 9, 10, 12, 8 }