the 1 isometry classes of irreducible [15,11,4]_4 codes are:

code no       1:
================
1 1 1 1 1 0 0 0 0 0 0 0 0 0 0
2 1 1 0 0 1 0 0 0 0 0 0 0 0 0
1 2 1 0 0 0 1 0 0 0 0 0 0 0 0
2 1 0 1 0 0 0 1 0 0 0 0 0 0 0
1 2 0 1 0 0 0 0 1 0 0 0 0 0 0
3 2 1 1 0 0 0 0 0 1 0 0 0 0 0
2 3 1 1 0 0 0 0 0 0 1 0 0 0 0
1 0 2 1 0 0 0 0 0 0 0 1 0 0 0
0 1 2 1 0 0 0 0 0 0 0 0 1 0 0
3 3 2 1 0 0 0 0 0 0 0 0 0 1 0
3 0 3 1 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 120
and is strongly generated by the following 5 elements:
(
2 0 0 0 
0 1 0 0 
0 2 1 2 
3 1 1 0 
, 1
, 
2 0 0 0 
1 0 1 2 
1 1 1 1 
2 1 3 3 
, 0
, 
0 3 0 0 
2 0 0 0 
2 1 1 0 
2 1 0 1 
, 0
, 
1 0 1 3 
0 1 0 0 
1 2 3 3 
3 1 1 0 
, 1
, 
3 3 3 3 
2 1 0 2 
0 0 3 0 
1 0 1 3 
, 1
)
acting on the columns of the generator matrix as follows (in order):
(3, 8, 5, 13)(4, 11, 14, 6)(7, 9, 10, 12), 
(2, 15)(3, 5)(4, 10)(6, 9)(7, 14)(8, 13)(11, 12), 
(1, 2)(3, 6)(4, 8)(5, 11)(13, 14), 
(1, 15)(3, 7, 5, 10)(4, 11, 14, 6)(8, 9, 13, 12), 
(1, 8, 13, 5)(2, 7, 14, 9)(4, 10, 11, 15)(6, 12)
orbits: { 1, 2, 15, 5, 9, 11, 8, 3, 7, 13, 6, 14, 4, 12, 10 }