the 1 isometry classes of irreducible [11,4,5]_2 codes are:

code no       1:
================
1 1 1 1 1 1 1 1 0 0 0
1 1 1 1 0 0 0 0 1 0 0
1 1 0 0 1 1 0 0 0 1 0
1 0 1 0 1 0 1 0 0 0 1
the automorphism group has order 48
and is strongly generated by the following 5 elements:
(
1 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 1 0 
0 0 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 1 0 0 0 0 
0 0 0 0 1 0 0 
0 0 0 0 0 0 1 
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 1 
1 1 1 1 1 1 1 
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 
1 0 0 0 0 0 0 
, 
0 0 0 0 0 1 0 
0 0 0 0 1 0 0 
1 1 1 1 1 1 1 
0 0 0 0 0 0 1 
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 1 0 0 
0 0 0 0 0 1 0 
1 0 0 0 0 0 0 
0 1 0 0 0 0 0 
0 0 0 0 0 0 1 
1 1 1 1 1 1 1 
0 0 1 0 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(3, 5)(4, 6)(9, 10), 
(2, 5, 3)(4, 6, 7)(9, 10, 11), 
(1, 7)(2, 8)(9, 10), 
(1, 6)(2, 5)(3, 8)(4, 7), 
(1, 3, 7, 5)(2, 4, 8, 6)(9, 10)
orbits: { 1, 7, 6, 5, 4, 3, 8, 2 }, { 9, 10, 11 }