the 1 isometry classes of irreducible [15,4,8]_2 codes are:

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