the 1 isometry classes of irreducible [12,6,6]_3 codes are:

code no       1:
================
1 1 1 1 1 0 2 0 0 0 0 0
2 2 1 1 0 1 0 2 0 0 0 0
2 1 2 0 1 1 0 0 2 0 0 0
1 2 0 2 1 1 0 0 0 2 0 0
1 0 2 1 2 1 0 0 0 0 2 0
0 1 1 2 2 1 0 0 0 0 0 2
the automorphism group has order 95040
and is strongly generated by the following 9 elements:
(
2 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 2 0 0 
2 1 0 1 2 2 
0 1 1 2 2 1 
, 
1 0 0 0 0 0 
0 2 0 0 0 0 
0 0 1 0 0 0 
0 0 0 2 0 0 
2 0 1 2 1 2 
2 1 0 1 2 2 
, 
1 0 0 0 0 0 
0 2 0 0 0 0 
0 0 2 0 0 0 
0 0 0 0 1 0 
1 0 2 1 2 1 
1 2 1 0 2 2 
, 
2 0 0 0 0 0 
0 1 0 0 0 0 
0 0 2 0 0 0 
1 2 1 0 2 2 
0 0 0 0 0 1 
1 2 0 2 1 1 
, 
1 0 0 0 0 0 
0 2 0 0 0 0 
0 0 0 0 1 0 
0 0 0 0 0 1 
0 0 0 2 0 0 
0 0 2 0 0 0 
, 
1 0 0 0 0 0 
1 2 1 0 2 2 
0 0 1 0 0 0 
1 1 1 1 1 0 
0 0 0 0 0 1 
0 0 0 0 1 0 
, 
1 0 0 0 0 0 
0 2 2 1 1 2 
2 2 2 2 2 0 
2 0 1 2 1 2 
1 2 1 0 2 2 
0 0 2 0 0 0 
, 
2 0 1 2 1 2 
2 2 2 2 2 0 
0 0 1 0 0 0 
2 1 2 0 1 1 
0 0 0 0 2 0 
0 0 0 0 0 2 
, 
1 2 1 0 2 2 
0 0 0 0 0 1 
0 0 2 0 0 0 
2 0 0 0 0 0 
0 1 0 0 0 0 
2 2 2 2 2 0 
)
acting on the columns of the generator matrix as follows (in order):
(5, 9, 7, 10)(6, 11, 8, 12), 
(5, 12, 7, 11)(6, 9, 8, 10), 
(4, 10, 11, 5)(6, 8, 7, 9), 
(4, 8, 11, 9)(5, 7, 10, 6), 
(3, 6, 4, 5)(7, 9, 8, 10), 
(2, 9)(4, 7)(5, 6)(10, 11), 
(2, 11, 4, 7, 3, 6, 10, 9, 5, 8, 12), 
(1, 10, 8, 11)(2, 9, 4, 7), 
(1, 4, 8, 9)(2, 5, 7, 6)
orbits: { 1, 11, 9, 6, 7, 10, 8, 2, 5, 12, 3, 4 }