the 2 isometry classes of irreducible [14,10,4]_4 codes are:

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

code no       2:
================
1 1 1 1 1 0 0 0 0 0 0 0 0 0
2 1 1 0 0 1 0 0 0 0 0 0 0 0
1 2 1 0 0 0 1 0 0 0 0 0 0 0
2 1 0 1 0 0 0 1 0 0 0 0 0 0
1 2 0 1 0 0 0 0 1 0 0 0 0 0
3 2 1 1 0 0 0 0 0 1 0 0 0 0
2 3 1 1 0 0 0 0 0 0 1 0 0 0
1 0 2 1 0 0 0 0 0 0 0 1 0 0
0 1 2 1 0 0 0 0 0 0 0 0 1 0
3 3 2 1 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 24
and is strongly generated by the following 4 elements:
(
2 0 0 0 
0 1 0 0 
3 1 3 0 
3 1 0 3 
, 0
, 
2 0 0 0 
0 1 0 0 
1 3 2 2 
2 0 3 2 
, 0
, 
3 0 0 0 
0 1 0 0 
3 2 0 3 
2 3 1 1 
, 1
, 
0 2 0 0 
2 0 0 0 
0 0 2 0 
0 0 0 2 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(3, 6, 7)(4, 8, 9)(5, 11, 10)(12, 14, 13), 
(3, 11, 7, 5, 6, 10)(4, 13, 9, 14, 8, 12), 
(3, 12, 5, 9)(4, 7, 14, 10)(6, 13, 11, 8), 
(1, 2)(6, 7)(8, 9)(10, 11)(12, 13)
orbits: { 1, 2 }, { 3, 7, 10, 9, 6, 11, 4, 14, 8, 13, 5, 12 }