the 4 isometry classes of irreducible [12,2,8]_3 codes are:

code no       1:
================
1 1 1 1 1 1 1 1 1 1 2 0
2 2 2 1 1 1 1 0 0 0 0 2
the automorphism group has order 6912
and is strongly generated by the following 11 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 
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 1 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 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 
1 1 1 1 1 1 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 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 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 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 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 
, 
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 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 
, 
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 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 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 
0 0 1 0 0 0 0 0 0 0 
2 2 2 2 2 2 2 2 2 2 
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 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 
, 
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 0 0 0 1 
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 
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 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 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 2 0 
0 0 0 0 0 0 0 0 0 2 
0 0 0 0 0 0 0 2 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(10, 11), 
(9, 11), 
(9, 11, 10), 
(8, 11, 9, 10), 
(6, 7)(8, 9), 
(5, 7)(8, 10, 9), 
(4, 6)(9, 10), 
(4, 7, 5)(8, 10), 
(4, 8, 6, 9, 5, 11)(7, 10), 
(2, 3)(4, 11, 7, 10)(5, 8, 6, 9), 
(1, 3, 2)(4, 6, 5, 7)(8, 10, 9)
orbits: { 1, 2, 3 }, { 4, 6, 5, 11, 10, 7, 8, 9 }, { 12 }

code no       2:
================
1 1 1 1 1 1 1 0 0 0 2 0
1 1 1 1 0 0 0 1 1 1 0 2
the automorphism group has order 82944
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 2 0 0 0 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 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 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 
, 
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 0 1 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 1 0 0 0 0 0 
2 2 2 2 2 2 2 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 
, 
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 2 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 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 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 1 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 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 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 
2 2 2 2 2 2 2 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 1 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 0 0 0 0 0 0 
0 0 0 0 2 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 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 1 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 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 
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 2 0 
1 1 1 1 0 0 0 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 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 1 0 0 0 
0 0 0 0 0 1 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):
(10, 12), 
(9, 10), 
(8, 9, 10), 
(7, 11)(8, 10, 9), 
(6, 7, 11), 
(5, 6, 7, 11)(8, 9), 
(5, 10)(6, 8, 7, 9)(11, 12), 
(3, 4)(9, 10), 
(2, 3)(6, 7, 11)(8, 10, 9), 
(1, 4, 2, 3)(6, 7, 11)(9, 10), 
(1, 11, 4, 5, 2, 7)(3, 6)(8, 9, 10), 
(1, 11, 12, 2, 7, 8, 4, 5, 10, 3, 6, 9)
orbits: { 1, 3, 7, 9, 4, 2, 6, 10, 11, 8, 5, 12 }

code no       3:
================
1 1 1 1 1 1 1 0 0 0 2 0
2 2 1 1 0 0 0 1 1 1 0 2
the automorphism group has order 9216
and is strongly generated by the following 13 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 
1 1 2 2 0 0 0 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 
, 
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 0 0 1 
0 0 0 0 0 0 0 1 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 
2 2 1 1 0 0 0 1 1 1 
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 
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 
, 
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 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 
1 1 1 1 1 1 1 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 
, 
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 2 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 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 
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 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 2 0 0 0 0 0 0 0 
0 0 0 2 0 0 0 0 0 0 
2 2 1 1 0 0 0 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 0 2 0 0 0 0 0 
0 0 0 0 0 2 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 1 0 0 0 0 
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 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 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 
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 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 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 0 0 
0 0 0 0 0 1 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 
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 0 0 2 
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), 
(8, 10, 9), 
(8, 10, 9, 12), 
(7, 11), 
(6, 7)(9, 10), 
(6, 11)(8, 9, 10), 
(5, 11, 6), 
(5, 6, 11, 7)(9, 10), 
(5, 9, 11, 12)(6, 10)(7, 8), 
(3, 4)(5, 7, 11, 6)(9, 10), 
(1, 2)(3, 4)(5, 7)(6, 11)(8, 9), 
(1, 4)(2, 3)(5, 6)(7, 11)(8, 10, 9)
orbits: { 1, 2, 4, 3 }, { 5, 6, 7, 12, 11, 10, 8, 9 }

code no       4:
================
1 1 1 1 1 1 1 0 0 0 2 0
2 2 1 1 1 0 0 1 1 1 0 2
the automorphism group has order 3456
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 
1 1 2 2 2 0 0 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 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 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 2 
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 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 1 0 0 0 
1 1 2 2 2 0 0 2 2 2 
0 0 0 0 0 0 0 1 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 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 0 0 1 
0 0 0 0 0 0 0 0 1 0 
0 0 0 0 0 0 0 1 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 
1 1 1 1 1 1 1 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 0 1 
0 0 0 0 0 0 0 1 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 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 0 1 
0 0 0 0 0 0 0 0 1 0 
0 0 0 0 0 0 0 1 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 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 0 2 0 0 
0 0 0 0 0 0 0 0 2 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 
2 2 2 2 2 2 2 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 0 0 2 
0 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 
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 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 2 
)
acting on the columns of the generator matrix as follows (in order):
(10, 12), 
(9, 10), 
(9, 10, 12), 
(8, 9, 10), 
(8, 9, 10, 12), 
(7, 11)(8, 10), 
(6, 11, 7)(8, 9), 
(4, 5)(8, 9, 10), 
(3, 4)(6, 7)(8, 10), 
(3, 5)(6, 7, 11), 
(3, 11)(4, 6)(5, 7)(8, 10), 
(1, 2)(3, 5, 4)(6, 7)(8, 9)
orbits: { 1, 2 }, { 3, 4, 5, 11, 6, 7 }, { 8, 10, 12, 9 }