the 1 isometry classes of irreducible [14,4,7]_2 codes are:

code no       1:
================
1 1 1 1 1 1 0 0 0 0 1 0 0 0
1 1 1 0 0 0 1 1 1 0 0 1 0 0
1 0 0 1 1 0 1 1 0 1 0 0 1 0
0 1 0 1 0 1 1 0 1 1 0 0 0 1
the automorphism group has order 1344
and is strongly generated by the following 6 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 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 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 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 
)
acting on the columns of the generator matrix as follows (in order):
(4, 7)(5, 8)(6, 9)(11, 12), 
(4, 5)(6, 11)(7, 8)(9, 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)
orbits: { 1, 6, 9, 11, 7, 4, 10, 12, 8, 3, 5, 13, 2, 14 }