the 1 isometry classes of irreducible [12,2,9]_3 codes are:

code no       1:
================
1 1 1 1 1 1 1 1 0 0 2 0
2 2 2 1 1 1 0 0 1 1 0 2
the automorphism group has order 31104
and is strongly generated by the following 13 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 2 1 1 1 0 0 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 
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 
2 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 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 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 
, 
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 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 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 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 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 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 
, 
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 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 
, 
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 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 2 
0 0 0 0 0 0 0 0 2 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 
2 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 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 2 
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 0 
0 0 0 0 0 0 1 0 0 0 
2 2 2 2 2 2 2 2 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 1 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 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 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 
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 0 0 0 0 1 
0 0 0 0 0 0 0 0 1 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 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 
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 0 0 0 1 0 
0 0 0 0 0 0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(10, 12), 
(9, 10), 
(8, 11)(9, 10), 
(7, 8), 
(7, 11), 
(7, 10, 8, 9)(11, 12), 
(5, 6)(7, 8), 
(4, 5, 6)(7, 8), 
(4, 11)(5, 7)(6, 8)(9, 10), 
(2, 3)(4, 11)(5, 7, 6, 8)(9, 10), 
(1, 3)(4, 8, 6, 11, 5, 7), 
(1, 3, 2)(4, 6)(7, 8, 11)(9, 10), 
(1, 5)(2, 4)(3, 6)(7, 8, 11)
orbits: { 1, 3, 2, 5, 6, 4, 7, 8, 11, 9, 10, 12 }