the 3 isometry classes of irreducible [17,14,3]_4 codes are:

code no       1:
================
1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
2 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
3 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0
2 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0
3 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0
2 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0
3 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0
0 2 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0
1 2 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0
2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0
3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 1152
and is strongly generated by the following 7 elements:
(
2 0 0 
0 3 0 
0 0 1 
, 1
, 
3 0 0 
0 2 0 
0 0 3 
, 1
, 
1 0 0 
0 1 0 
1 1 1 
, 1
, 
3 0 0 
0 2 0 
1 2 2 
, 1
, 
1 0 0 
0 3 0 
3 3 2 
, 0
, 
3 0 0 
3 2 2 
1 2 0 
, 0
, 
1 0 0 
2 1 3 
0 1 1 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(4, 17)(5, 6)(8, 10)(11, 14)(12, 16)(13, 15), 
(4, 15)(5, 7)(9, 10)(11, 14)(12, 17)(13, 16), 
(3, 4)(6, 7)(8, 11)(9, 12)(10, 13)(14, 15), 
(3, 12)(4, 8)(5, 7)(9, 11)(10, 13)(14, 16), 
(3, 13, 16)(4, 15, 8)(5, 7, 6)(9, 11, 17)(10, 12, 14), 
(2, 9, 12)(3, 13, 7)(4, 6, 10)(5, 8, 11), 
(2, 17)(3, 12, 9, 4, 8, 11)(5, 14, 6, 16, 7, 15)(10, 13)
orbits: { 1 }, { 2, 12, 17, 16, 9, 3, 10, 4, 11, 13, 14, 6, 7, 8, 15, 5 }

code no       2:
================
1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
2 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
3 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0
2 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0
3 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0
2 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0
3 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0
0 2 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0
1 2 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0
2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0
0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 36
and is strongly generated by the following 4 elements:
(
2 0 0 
0 3 0 
0 3 3 
, 1
, 
1 0 0 
2 1 1 
1 0 1 
, 1
, 
2 0 0 
2 3 3 
1 0 3 
, 1
, 
0 3 1 
3 3 0 
3 2 0 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(3, 11)(4, 9)(5, 6)(8, 12)(10, 13)(15, 16), 
(2, 13)(3, 8)(4, 7)(5, 12)(6, 11)(14, 16), 
(2, 12)(3, 10)(4, 7)(5, 11)(6, 13)(14, 15), 
(1, 17)(2, 11, 13, 8, 10, 5)(3, 12, 6)(4, 16, 9, 15, 7, 14)
orbits: { 1, 17 }, { 2, 13, 12, 5, 10, 6, 11, 8, 3 }, { 4, 9, 7, 14, 16, 15 }

code no       3:
================
1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
2 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
3 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0
2 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0
3 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0
2 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0
3 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0
0 2 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0
1 2 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0
0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0
1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 48
and is strongly generated by the following 5 elements:
(
1 0 0 
0 1 0 
0 0 1 
, 1
, 
1 0 0 
0 1 0 
0 1 1 
, 1
, 
1 0 0 
0 1 0 
1 1 1 
, 1
, 
1 0 0 
1 1 0 
3 1 1 
, 1
, 
0 1 0 
1 0 0 
0 1 1 
, 1
)
acting on the columns of the generator matrix as follows (in order):
(6, 7)(9, 10)(12, 13)(14, 16)(15, 17), 
(3, 11)(4, 8)(6, 7)(9, 13)(10, 12), 
(3, 4)(6, 7)(8, 11)(9, 12)(10, 13)(14, 15)(16, 17), 
(2, 5)(3, 12)(4, 9)(8, 13)(10, 11)(14, 15), 
(1, 2)(3, 8, 4, 11)(9, 17, 13, 14)(10, 15, 12, 16)
orbits: { 1, 2, 5 }, { 3, 11, 4, 12, 8, 10, 9, 13, 15, 16, 14, 17 }, { 6, 7 }