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

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