the 2 isometry classes of irreducible [12,7,4]_2 codes are:

code no       1:
================
1 1 1 1 1 1 0 0 0 0 0 0
1 1 1 0 0 0 1 0 0 0 0 0
1 1 0 1 0 0 0 1 0 0 0 0
1 0 1 1 0 0 0 0 1 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0
1 1 0 0 1 0 0 0 0 0 1 0
1 0 1 0 1 0 0 0 0 0 0 1
the automorphism group has order 192
and is strongly generated by the following 7 elements:
(
1 0 0 0 0 
0 1 0 0 0 
1 1 1 0 0 
0 0 0 1 0 
1 1 0 0 1 
, 
1 0 0 0 0 
0 1 0 0 0 
0 1 1 1 0 
0 0 0 1 0 
0 0 0 0 1 
, 
1 0 0 0 0 
1 0 1 1 0 
1 1 0 1 0 
0 0 0 1 0 
1 1 1 1 1 
, 
1 0 0 0 0 
0 1 1 1 0 
0 0 1 0 0 
0 0 0 1 0 
0 0 0 0 1 
, 
1 0 0 0 0 
0 0 1 0 0 
1 1 1 0 0 
0 0 0 1 0 
1 0 1 0 1 
, 
1 1 1 0 0 
1 1 0 1 0 
1 0 1 1 0 
0 1 1 1 0 
1 1 1 1 1 
, 
1 0 1 1 0 
1 0 0 0 0 
1 1 1 0 0 
0 0 1 0 0 
1 1 1 1 1 
)
acting on the columns of the generator matrix as follows (in order):
(3, 7)(5, 11)(9, 10), 
(3, 10)(6, 12)(7, 9), 
(2, 9)(3, 8)(5, 6), 
(2, 10)(6, 11)(7, 8), 
(2, 7, 3)(5, 11, 12)(8, 10, 9), 
(1, 7)(2, 8)(3, 9)(4, 10)(5, 6), 
(1, 2, 10, 9)(3, 4, 8, 7)(5, 6)
orbits: { 1, 7, 9, 3, 8, 2, 10, 4 }, { 5, 11, 6, 12 }

code no       2:
================
1 1 1 1 1 1 0 0 0 0 0 0
1 1 1 0 0 0 1 0 0 0 0 0
1 1 0 1 0 0 0 1 0 0 0 0
1 0 1 1 0 0 0 0 1 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0
1 1 0 0 1 0 0 0 0 0 1 0
0 0 1 1 1 0 0 0 0 0 0 1
the automorphism group has order 2304
and is strongly generated by the following 8 elements:
(
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
1 1 1 1 1 
, 
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
0 0 1 1 1 
, 
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
1 1 0 1 0 
1 1 0 0 1 
, 
1 0 0 0 0 
0 1 0 0 0 
0 0 0 1 0 
0 0 1 0 0 
0 0 0 0 1 
, 
1 0 0 0 0 
0 1 0 0 0 
0 0 1 1 1 
1 1 0 0 1 
1 1 1 0 0 
, 
1 0 0 0 0 
1 0 1 1 0 
0 0 1 0 0 
1 1 1 0 0 
1 1 1 1 1 
, 
1 0 1 1 0 
0 1 1 1 0 
1 1 1 0 0 
1 1 0 1 0 
0 0 0 0 1 
, 
1 1 1 0 0 
1 1 0 1 0 
1 0 0 0 0 
0 1 0 0 0 
1 1 1 1 1 
)
acting on the columns of the generator matrix as follows (in order):
(5, 6)(11, 12), 
(5, 12)(6, 11), 
(4, 8)(5, 11)(9, 10), 
(3, 4)(7, 8), 
(3, 11, 4, 12)(5, 8, 6, 7)(9, 10), 
(2, 9)(4, 7)(5, 6), 
(1, 9)(2, 10)(3, 7)(4, 8), 
(1, 3, 9, 7)(2, 4, 10, 8)(5, 6)
orbits: { 1, 9, 7, 10, 2, 3, 8, 6, 4, 12, 5, 11 }