the 1 isometry classes of irreducible [12,1,12]_3 codes are:

code no       1:
================
1 1 1 1 1 1 1 1 1 1 1 2
the automorphism group has order 479001600
and is strongly generated by the following 21 elements:
(
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 
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 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 0 0 0 1 0 
2 2 2 2 2 2 2 2 2 2 2 
, 
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 
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 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 0 0 0 0 1 
0 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 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 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 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 1 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 
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 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 1 0 
0 0 0 0 0 0 0 0 1 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 
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 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 1 0 
0 0 0 0 0 0 0 0 1 0 0 
0 0 0 0 0 0 0 0 0 0 1 
, 
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 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 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 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 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 0 2 0 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 1 
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 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 
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 0 0 0 0 0 0 0 1 
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 1 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 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 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 2 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 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 0 0 0 1 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 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 1 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 
, 
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 
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 1 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 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 
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 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 0 0 0 2 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 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 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 0 0 0 2 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 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 
, 
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 0 2 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 0 0 0 0 2 
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 2 0 0 0 0 0 
0 0 0 0 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 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 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 0 0 0 0 0 1 
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 1 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 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 2 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 2 
0 0 2 0 0 0 0 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 0 0 0 0 0 0 2 0 0 0 
, 
1 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 1 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 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 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 1 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 1 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 0 0 0 2 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 2 0 0 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 0 0 0 2 0 0 0 
0 2 0 0 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 0 0 1 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 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 0 1 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 
1 0 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 2 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 2 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 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 2 0 0 0 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 
2 0 0 0 0 0 0 0 0 0 0 
, 
1 1 1 1 1 1 1 1 1 1 1 
0 0 0 0 0 0 0 0 2 0 0 
0 2 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 2 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 0 0 0 0 0 0 2 
0 0 0 0 0 0 2 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 
)
acting on the columns of the generator matrix as follows (in order):
(11, 12), 
(10, 11), 
(10, 11, 12), 
(9, 11), 
(9, 10), 
(8, 11), 
(8, 12)(9, 11, 10), 
(7, 11)(8, 9, 10), 
(7, 10, 9)(8, 11), 
(7, 10, 11, 8, 9, 12), 
(6, 8), 
(6, 8, 11, 10, 7, 9), 
(5, 9, 7)(6, 8), 
(5, 11, 7, 6, 10), 
(4, 9, 10, 5, 7, 6, 11, 8), 
(3, 8, 11, 7)(4, 10, 9, 5), 
(2, 3, 10, 11, 7)(4, 5)(6, 9), 
(2, 10, 3, 6)(5, 8, 9, 7), 
(1, 9, 10)(2, 5, 7, 11, 8, 4)(3, 6), 
(1, 11, 9, 7, 10, 2, 4, 8, 5, 3), 
(1, 11, 7, 8, 12)(2, 3, 5, 6, 9)(4, 10)
orbits: { 1, 10, 3, 12, 11, 9, 7, 6, 4, 2, 5, 8 }