the 6 isometry classes of irreducible [14,5,8]_4 codes are:

code no       1:
================
1 1 1 1 1 1 1 1 1 1 0 0 0 0
3 2 2 2 1 1 1 0 0 0 1 0 0 0
2 3 2 1 2 1 0 1 0 0 0 1 0 0
2 2 3 1 1 2 0 0 1 0 0 0 1 0
3 2 2 1 0 0 2 1 1 0 0 0 0 1
the automorphism group has order 96
and is strongly generated by the following 5 elements:
(
1 0 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 1 0 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 1 0 0 
0 0 0 0 0 0 0 0 1 
0 0 0 0 0 0 0 1 0 
, 0
, 
2 0 0 0 0 0 0 0 0 
3 3 2 1 1 3 0 0 1 
3 2 3 1 3 1 0 1 0 
0 0 0 1 0 0 0 0 0 
0 0 0 0 0 0 0 0 2 
0 0 0 0 0 0 0 2 0 
1 2 2 2 3 3 3 0 0 
0 0 0 0 2 0 0 0 0 
0 0 0 0 0 2 0 0 0 
, 1
, 
3 0 0 0 0 0 0 0 0 
0 0 0 0 0 3 0 0 0 
0 0 0 0 3 0 0 0 0 
0 0 0 2 0 0 0 0 0 
0 0 3 0 0 0 0 0 0 
0 3 0 0 0 0 0 0 0 
0 0 0 0 0 0 1 0 0 
1 3 1 2 1 2 0 2 0 
1 1 3 2 2 1 0 0 2 
, 1
, 
1 1 2 3 3 1 0 0 3 
0 0 0 1 0 0 0 0 0 
0 0 0 0 0 0 3 0 0 
0 0 0 0 0 0 0 0 1 
3 0 0 0 0 0 0 0 0 
3 2 2 2 1 1 1 0 0 
3 1 3 2 3 2 0 2 0 
0 0 1 0 0 0 0 0 0 
0 0 0 0 3 0 0 0 0 
, 0
, 
0 0 0 0 0 1 0 0 0 
3 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 2 0 0 
0 0 1 0 0 0 0 0 0 
0 0 0 2 0 0 0 0 0 
1 2 2 2 3 3 3 0 0 
0 0 0 0 3 0 0 0 0 
0 0 0 0 0 0 0 1 0 
3 3 2 1 1 3 0 0 1 
, 1
)
acting on the columns of the generator matrix as follows (in order):
(2, 3)(5, 6)(8, 9)(12, 13), 
(2, 12, 3, 13)(5, 8, 6, 9)(7, 11), 
(2, 6)(3, 5)(8, 12)(9, 13)(10, 14), 
(1, 5, 9, 4, 2, 13)(3, 8, 11, 6, 12, 7), 
(1, 2, 11, 6)(3, 4, 5, 7)(9, 13)
orbits: { 1, 13, 6, 12, 3, 9, 2, 5, 8, 11, 7, 4 }, { 10, 14 }

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

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

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

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

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