the 1 isometry classes of irreducible [15,11,3]_2 codes are:

code no       1:
================
1 1 1 1 1 0 0 0 0 0 0 0 0 0 0
1 1 0 0 0 1 0 0 0 0 0 0 0 0 0
1 0 1 0 0 0 1 0 0 0 0 0 0 0 0
0 1 1 0 0 0 0 1 0 0 0 0 0 0 0
1 1 1 0 0 0 0 0 1 0 0 0 0 0 0
1 0 0 1 0 0 0 0 0 1 0 0 0 0 0
0 1 0 1 0 0 0 0 0 0 1 0 0 0 0
1 1 0 1 0 0 0 0 0 0 0 1 0 0 0
0 0 1 1 0 0 0 0 0 0 0 0 1 0 0
1 0 1 1 0 0 0 0 0 0 0 0 0 1 0
0 1 1 1 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 20160
and is strongly generated by the following 11 elements:
(
1 0 0 0 
0 1 0 0 
0 0 1 0 
0 1 0 1 
, 
1 0 0 0 
0 1 0 0 
0 0 1 0 
1 1 1 1 
, 
1 0 0 0 
0 1 0 0 
0 0 1 0 
1 1 0 1 
, 
1 0 0 0 
0 1 0 0 
0 1 1 0 
0 1 0 1 
, 
1 0 0 0 
0 1 0 0 
1 0 1 0 
1 0 0 1 
, 
1 0 0 0 
0 1 0 0 
0 0 0 1 
0 0 1 0 
, 
1 0 0 0 
0 1 0 0 
0 1 1 1 
0 1 0 1 
, 
1 0 0 0 
0 0 1 0 
0 0 0 1 
0 1 0 0 
, 
1 0 0 0 
1 1 0 0 
0 1 1 0 
1 1 0 1 
, 
0 0 0 1 
1 1 0 1 
0 1 0 1 
1 1 1 1 
, 
0 1 1 1 
1 1 1 1 
1 0 1 0 
1 1 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(4, 11)(5, 14)(10, 12)(13, 15), 
(4, 5)(10, 15)(11, 14)(12, 13), 
(4, 12)(5, 13)(10, 11)(14, 15), 
(3, 8)(4, 11)(7, 9)(10, 12), 
(3, 7)(4, 10)(8, 9)(11, 12), 
(3, 4)(7, 10)(8, 11)(9, 12), 
(3, 13, 8, 15)(4, 11)(5, 7, 14, 9)(10, 12), 
(2, 4, 3)(6, 10, 7)(8, 11, 13)(9, 12, 14), 
(2, 6)(3, 9, 7, 8)(4, 11, 10, 12)(13, 14), 
(1, 8, 5, 4)(2, 7, 13, 12)(3, 11)(9, 10), 
(1, 6, 4, 14, 10, 15)(2, 12, 7, 3, 9, 5)(8, 13, 11)
orbits: { 1, 4, 15, 11, 5, 12, 10, 3, 2, 6, 13, 14, 8, 9, 7 }