the 1 isometry classes of irreducible [14,7,6]_3 codes are:

code no       1:
================
1 1 1 1 1 1 1 2 0 0 0 0 0 0
2 2 1 1 1 0 0 0 2 0 0 0 0 0
2 1 2 1 0 1 0 0 0 2 0 0 0 0
1 2 2 1 0 0 1 0 0 0 2 0 0 0
2 1 0 2 2 1 1 0 0 0 0 2 0 0
1 0 2 2 1 2 1 0 0 0 0 0 2 0
0 1 2 1 2 2 1 0 0 0 0 0 0 2
the automorphism group has order 1092
and is strongly generated by the following 4 elements:
(
1 0 0 0 0 0 0 
0 1 0 0 0 0 0 
2 2 2 2 2 2 2 
0 0 1 0 0 0 0 
1 2 1 2 0 2 0 
1 2 0 1 1 2 2 
1 2 2 1 0 0 1 
, 
1 0 0 0 0 0 0 
1 2 2 1 0 0 1 
0 0 0 0 0 0 1 
0 1 0 0 0 0 0 
0 0 0 0 0 2 0 
0 0 0 2 0 0 0 
2 1 0 2 2 1 1 
, 
0 0 2 0 0 0 0 
1 2 0 1 1 2 2 
0 0 0 0 0 0 1 
0 0 0 0 0 2 0 
1 2 2 1 0 0 1 
2 2 2 2 2 2 2 
2 0 0 0 0 0 0 
, 
0 2 1 2 1 1 2 
1 1 1 1 1 1 1 
0 0 0 0 0 0 2 
0 0 0 1 0 0 0 
0 0 0 0 1 0 0 
2 0 0 0 0 0 0 
1 2 2 1 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(3, 4, 14, 11, 7, 8)(5, 12, 6, 13, 9, 10), 
(2, 4, 6, 5, 13, 11)(3, 10, 9, 8, 12, 7), 
(1, 7, 3)(2, 10, 12)(4, 8, 6)(5, 9, 11), 
(1, 6, 14)(2, 10, 8)(3, 11, 7)(9, 12, 13)
orbits: { 1, 3, 14, 8, 7, 4, 6, 9, 10, 11, 12, 2, 13, 5 }