the 1 isometry classes of irreducible [15,10,4]_2 codes are:

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