the 1 isometry classes of irreducible [15,5,7]_2 codes are:

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