the 1 isometry classes of irreducible [14,9,4]_2 codes are:

code no       1:
================
1 1 1 1 1 1 0 0 0 0 0 0 0 0
1 1 1 0 0 0 1 0 0 0 0 0 0 0
1 1 0 1 0 0 0 1 0 0 0 0 0 0
1 0 1 1 0 0 0 0 1 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0
1 1 0 0 1 0 0 0 0 0 1 0 0 0
1 0 1 0 1 0 0 0 0 0 0 1 0 0
0 1 1 0 1 0 0 0 0 0 0 0 1 0
1 0 0 1 1 0 0 0 0 0 0 0 0 1
the automorphism group has order 2688
and is strongly generated by the following 8 elements:
(
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
0 1 1 0 1 
, 
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
1 1 0 1 0 
1 1 0 0 1 
, 
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 1 1 1 0 
0 1 1 0 1 
, 
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 0 1 0 0 
0 1 0 0 0 
1 1 0 0 1 
1 1 0 1 0 
, 
1 0 0 0 0 
0 1 1 1 0 
0 0 0 1 0 
0 0 1 0 0 
0 0 0 0 1 
, 
1 1 0 1 0 
0 1 1 1 0 
0 0 0 1 0 
0 1 0 0 0 
0 0 0 0 1 
, 
1 0 0 1 1 
0 0 0 0 1 
0 1 1 0 1 
1 0 1 1 0 
1 0 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(5, 13)(6, 14)(11, 12), 
(4, 8)(5, 11)(9, 10)(12, 13), 
(4, 10)(5, 13)(8, 9)(11, 12), 
(4, 12)(5, 9)(8, 13)(10, 11), 
(2, 3)(4, 12, 10, 11)(5, 9, 13, 8), 
(2, 10)(3, 4)(6, 11)(12, 14), 
(1, 9, 7, 8)(2, 4, 3, 10)(11, 12), 
(1, 5, 2, 9, 4, 11, 6, 7, 13, 3, 8, 10, 12, 14)
orbits: { 1, 8, 14, 4, 9, 13, 7, 3, 6, 12, 10, 11, 2, 5 }