the 1 isometry classes of irreducible [14,10,3]_2 codes are:

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