the 2 isometry classes of irreducible [11,6,4]_2 codes are:

code no       1:
================
1 1 1 1 1 1 0 0 0 0 0
1 1 1 0 0 0 1 0 0 0 0
1 1 0 1 0 0 0 1 0 0 0
1 0 1 1 0 0 0 0 1 0 0
0 1 1 1 0 0 0 0 0 1 0
1 1 0 0 1 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 
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 
1 1 1 0 0 
1 1 0 1 0 
0 0 0 0 1 
, 
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 
, 
0 1 0 0 0 
0 1 1 1 0 
0 0 0 1 0 
1 1 0 1 0 
1 1 1 1 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):
(4, 8)(5, 11)(9, 10), 
(3, 4)(7, 8), 
(3, 7)(4, 8), 
(2, 9)(4, 7)(5, 6), 
(1, 9)(2, 10)(3, 7)(4, 8), 
(1, 9, 10, 2)(3, 7, 8, 4)(5, 6), 
(1, 3, 9, 7)(2, 4, 10, 8)(5, 6)
orbits: { 1, 9, 2, 7, 10, 3, 8, 4 }, { 5, 11, 6 }

code no       2:
================
1 1 1 1 1 1 0 0 0 0 0
1 1 1 0 0 0 1 0 0 0 0
1 1 0 1 0 0 0 1 0 0 0
1 0 1 1 0 0 0 0 1 0 0
1 1 0 0 1 0 0 0 0 1 0
1 0 1 0 1 0 0 0 0 0 1
the automorphism group has order 120
and is strongly generated by the following 5 elements:
(
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 0 0 1 
0 0 0 1 0 
, 
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 
1 1 0 1 0 
1 0 1 1 0 
1 1 1 1 1 
0 0 0 1 0 
, 
1 1 1 1 1 
0 0 0 0 1 
0 0 0 1 0 
0 0 1 0 0 
0 1 0 0 0 
, 
1 0 1 0 1 
0 0 0 0 1 
0 1 0 0 0 
0 0 0 1 0 
0 0 1 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(4, 5)(8, 10)(9, 11), 
(2, 9)(3, 8)(5, 6), 
(2, 10, 9, 3, 11, 8)(4, 5, 6), 
(1, 6)(2, 5)(3, 4)(9, 10), 
(1, 10, 11)(2, 3, 5)(6, 9, 8)
orbits: { 1, 6, 11, 5, 8, 9, 3, 10, 4, 2 }, { 7 }