the 1 isometry classes of irreducible [11,6,5]_4 codes are:

code no       1:
================
1 1 1 1 1 1 0 0 0 0 0
2 2 1 1 0 0 1 0 0 0 0
3 2 1 0 1 0 0 1 0 0 0
2 0 3 1 1 0 0 0 1 0 0
1 2 0 2 1 0 0 0 0 1 0
3 1 2 3 1 0 0 0 0 0 1
the automorphism group has order 110
and is strongly generated by the following 4 elements:
(
1 0 0 0 0 
0 0 2 0 0 
3 1 2 3 1 
1 1 1 1 1 
3 0 1 2 2 
, 0
, 
1 0 0 0 0 
0 0 0 0 3 
3 0 2 1 1 
2 1 0 1 2 
0 0 2 0 0 
, 1
, 
3 3 1 1 0 
1 2 3 0 3 
0 0 0 0 2 
0 0 3 0 0 
1 1 1 1 1 
, 1
, 
3 1 2 3 1 
3 3 2 2 0 
0 3 0 0 0 
0 0 0 0 2 
3 1 0 1 3 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(2, 10, 8, 11, 3)(4, 7, 9, 5, 6), 
(2, 6, 10, 4, 8, 7, 11, 9, 3, 5), 
(1, 6, 5, 3, 4, 9, 8, 2, 10, 7), 
(1, 6, 10, 5, 4, 7, 2, 3, 8, 9, 11)
orbits: { 1, 7, 11, 4, 8, 10, 9, 6, 3, 5, 2 }