the 1 isometry classes of irreducible [11,5,6]_3 codes are:

code no       1:
================
1 1 1 1 1 0 2 0 0 0 0
2 2 1 1 0 1 0 2 0 0 0
2 1 2 0 1 1 0 0 2 0 0
1 2 0 2 1 1 0 0 0 2 0
1 0 2 1 2 1 0 0 0 0 2
the automorphism group has order 7920
and is strongly generated by the following 8 elements:
(
2 0 0 0 0 0 
0 2 0 0 0 0 
0 0 2 0 0 0 
2 0 1 2 1 2 
2 1 0 1 2 2 
1 1 1 1 1 0 
, 
1 0 0 0 0 0 
0 2 0 0 0 0 
0 0 1 0 0 0 
2 1 2 0 1 1 
0 0 0 0 0 2 
2 1 0 1 2 2 
, 
1 0 0 0 0 0 
0 2 0 0 0 0 
0 0 2 0 0 0 
0 0 0 0 1 0 
1 0 2 1 2 1 
1 2 1 0 2 2 
, 
1 0 0 0 0 0 
0 2 0 0 0 0 
0 0 0 0 1 0 
0 0 0 0 0 1 
0 0 0 2 0 0 
0 0 2 0 0 0 
, 
1 0 0 0 0 0 
0 2 0 0 0 0 
2 2 2 2 2 0 
1 1 2 2 0 2 
2 1 2 0 1 1 
1 2 0 2 1 1 
, 
2 0 0 0 0 0 
1 1 2 2 0 2 
0 0 0 0 0 2 
0 0 0 2 0 0 
1 1 1 1 1 0 
0 1 0 0 0 0 
, 
1 2 1 0 2 2 
0 0 0 0 0 1 
0 0 2 0 0 0 
2 0 0 0 0 0 
0 1 0 0 0 0 
2 2 2 2 2 0 
, 
2 0 1 2 1 2 
2 2 2 2 2 0 
0 0 1 0 0 0 
2 1 2 0 1 1 
0 0 0 0 2 0 
0 0 0 0 0 2 
)
acting on the columns of the generator matrix as follows (in order):
(4, 11)(5, 10)(6, 7)(8, 9), 
(4, 8, 11, 9)(5, 7, 10, 6), 
(4, 10, 11, 5)(6, 8, 7, 9), 
(3, 6, 4, 5)(7, 9, 8, 10), 
(3, 8, 4, 7)(5, 10, 6, 9), 
(2, 6, 3, 8)(5, 9, 10, 7), 
(1, 4, 8, 9)(2, 5, 7, 6), 
(1, 10, 8, 11)(2, 9, 4, 7)
orbits: { 1, 9, 11, 8, 7, 6, 5, 2, 4, 10, 3 }