the 3 isometry classes of irreducible [11,2,6]_2 codes are:

code no       1:
================
1 1 1 1 1 1 1 1 1 1 0
1 1 1 1 1 0 0 0 0 0 1
the automorphism group has order 28800
and is strongly generated by the following 11 elements:
(
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 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 1 0 0 
0 0 0 0 0 0 0 1 0 
1 1 1 1 1 1 1 1 1 
, 
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 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 1 0 0 
0 0 0 0 0 0 0 0 1 
0 0 0 0 0 0 0 1 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 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 1 0 0 
1 1 1 1 1 1 1 1 1 
0 0 0 0 0 0 0 1 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 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 1 0 
1 1 1 1 1 1 1 1 1 
0 0 0 0 0 0 0 0 1 
, 
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 1 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 0 0 0 1 
0 0 0 0 0 0 0 1 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 1 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 
1 1 1 1 1 1 1 1 1 
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 
, 
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 1 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 1 0 0 0 
0 0 0 0 0 0 0 0 1 
0 0 0 0 0 0 1 0 0 
, 
1 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 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 1 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 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 1 0 0 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 1 0 
1 1 1 1 1 1 1 1 1 
, 
1 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 1 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 0 
1 1 1 1 1 1 1 1 1 
0 0 0 0 0 0 1 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 0 1 
0 0 0 0 0 1 0 0 0 
1 1 1 1 1 1 1 1 1 
0 0 0 0 0 0 0 1 0 
0 0 0 0 0 0 1 0 0 
0 1 0 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 1 0 0 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(9, 10), 
(8, 9), 
(8, 9, 10), 
(7, 10, 8), 
(6, 7)(8, 9), 
(6, 10), 
(4, 5)(6, 7, 9, 8), 
(3, 5)(6, 8, 7, 9), 
(3, 4)(6, 10, 9), 
(2, 5, 3, 4)(6, 9, 10), 
(1, 10, 3, 8, 4, 9)(2, 6)(5, 7)
orbits: { 1, 9, 10, 8, 7, 6, 4, 3, 5, 2 }, { 11 }

code no       2:
================
1 1 1 1 1 0 0 0 0 1 0
1 1 0 0 0 1 1 1 1 0 1
the automorphism group has order 5760
and is strongly generated by the following 11 elements:
(
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 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 1 0 0 
0 0 0 0 0 0 0 1 0 
1 1 0 0 0 1 1 1 1 
, 
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 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 1 0 0 
0 0 0 0 0 0 0 0 1 
0 0 0 0 0 0 0 1 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 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 1 0 0 
1 1 0 0 0 1 1 1 1 
0 0 0 0 0 0 0 1 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 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 1 0 
0 0 0 0 0 0 0 0 1 
0 0 0 0 0 0 1 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 1 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 
0 0 0 0 0 1 0 0 0 
1 1 0 0 0 1 1 1 1 
0 0 0 0 0 0 0 1 0 
0 0 0 0 0 0 0 0 1 
, 
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 1 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 1 0 0 0 
0 0 0 0 0 0 0 1 0 
0 0 0 0 0 0 1 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 1 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 
1 1 0 0 0 1 1 1 1 
0 0 0 0 0 0 0 0 1 
0 0 0 0 0 0 1 0 0 
0 0 0 0 0 1 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 1 0 0 0 0 0 
1 1 1 1 1 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 0 0 1 
0 0 0 0 0 1 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 
1 1 1 1 1 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 1 0 0 0 
0 0 0 0 0 0 0 1 0 
, 
1 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 1 0 0 0 0 0 
1 1 1 1 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 1 
0 0 0 0 0 0 0 1 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 1 0 0 0 0 0 
1 1 1 1 1 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 1 0 
0 0 0 0 0 0 1 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(9, 11), 
(8, 9), 
(8, 9, 11), 
(7, 9, 8), 
(7, 11), 
(6, 7, 9), 
(6, 9, 7, 8, 11), 
(5, 10)(6, 9, 8), 
(4, 10)(6, 8, 9, 7), 
(3, 10, 5)(8, 9), 
(1, 2)(5, 10)(7, 9)
orbits: { 1, 2 }, { 3, 5, 10, 4 }, { 6, 9, 11, 8, 7 }

code no       3:
================
1 1 1 1 1 0 0 0 0 1 0
1 1 1 0 0 1 1 1 1 0 1
the automorphism group has order 8640
and is strongly generated by the following 10 elements:
(
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 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 1 0 0 
0 0 0 0 0 0 0 1 0 
1 1 1 0 0 1 1 1 1 
, 
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 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 1 0 0 
0 0 0 0 0 0 0 0 1 
0 0 0 0 0 0 0 1 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 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 1 
0 0 0 0 0 0 0 1 0 
0 0 0 0 0 0 1 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 1 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 
0 0 0 0 0 1 0 0 0 
1 1 1 0 0 1 1 1 1 
0 0 0 0 0 0 1 0 0 
0 0 0 0 0 0 0 0 1 
, 
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 1 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 1 0 0 
0 0 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 1 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 1 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 
1 1 1 0 0 1 1 1 1 
0 0 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 0 1 
0 0 0 0 0 0 1 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 1 0 0 0 0 0 
1 1 1 1 1 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 1 0 0 0 
0 0 0 0 0 0 1 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 1 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 1 0 
0 0 0 0 0 0 1 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 1 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 
1 1 1 1 1 0 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 0 1 
0 0 0 0 0 0 1 0 0 
, 
0 0 0 1 0 0 0 0 0 
1 1 1 1 1 0 0 0 0 
0 0 0 0 1 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 1 
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 
)
acting on the columns of the generator matrix as follows (in order):
(9, 11), 
(8, 9), 
(7, 9), 
(7, 8, 11), 
(6, 8, 9), 
(6, 7, 9, 8, 11), 
(5, 10)(6, 8)(7, 9), 
(4, 5)(6, 9)(7, 8), 
(2, 3)(5, 10)(6, 7, 9, 8), 
(1, 10, 2, 4)(3, 5)(6, 8, 9)
orbits: { 1, 4, 5, 2, 10, 3 }, { 6, 9, 11, 8, 7 }