the 2 isometry classes of irreducible [17,9,7]_4 codes are:

code no       1:
================
1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0
2 2 2 1 1 1 0 0 0 1 0 0 0 0 0 0 0
3 2 1 2 1 0 1 0 0 0 1 0 0 0 0 0 0
2 3 1 1 2 0 0 1 0 0 0 1 0 0 0 0 0
2 2 1 0 0 2 1 1 0 0 0 0 1 0 0 0 0
3 2 0 1 0 1 2 1 0 0 0 0 0 1 0 0 0
1 3 3 2 1 3 2 1 0 0 0 0 0 0 1 0 0
2 3 2 3 1 2 3 1 0 0 0 0 0 0 0 1 0
1 2 0 0 3 3 3 1 0 0 0 0 0 0 0 0 1
the automorphism group has order 960
and is strongly generated by the following 7 elements:
(
1 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 
0 0 0 0 0 0 1 0 
0 0 0 0 0 0 0 1 
0 0 1 0 0 0 0 0 
0 0 0 1 0 0 0 0 
0 0 0 0 1 0 0 0 
, 0
, 
3 0 0 0 0 0 0 0 
0 3 0 0 0 0 0 0 
1 1 2 0 0 1 2 2 
3 1 0 2 0 2 1 2 
1 3 0 0 2 2 2 1 
1 1 1 2 2 2 0 0 
3 1 2 1 2 0 2 0 
1 3 2 2 1 0 0 2 
, 1
, 
2 0 0 0 0 0 0 0 
0 0 0 0 1 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 0 3 
1 3 1 3 2 1 3 2 
2 3 3 1 2 3 1 2 
3 2 1 1 3 0 0 1 
, 1
, 
1 0 0 0 0 0 0 0 
0 0 0 0 0 0 2 0 
0 0 0 0 2 0 0 0 
2 1 3 1 3 0 3 0 
0 0 0 1 0 0 0 0 
0 1 0 0 0 0 0 0 
2 1 1 3 2 1 3 2 
2 2 1 0 0 2 1 1 
, 0
, 
2 3 1 3 1 0 1 0 
0 0 1 0 0 0 0 0 
2 3 0 1 0 1 3 1 
2 1 3 3 2 0 0 3 
0 3 0 0 0 0 0 0 
2 2 3 0 0 2 3 3 
0 0 0 2 0 0 0 0 
1 1 1 2 2 2 0 0 
, 1
, 
3 3 3 2 2 2 0 0 
1 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 2 
1 2 1 2 3 1 2 3 
2 1 0 3 0 3 1 3 
2 3 1 1 2 0 0 1 
0 0 0 1 0 0 0 0 
0 0 0 0 0 3 0 0 
, 0
, 
3 2 0 0 1 1 1 3 
3 2 3 2 1 3 2 1 
0 0 0 0 3 0 0 0 
1 2 2 3 1 2 3 1 
1 1 2 0 0 1 2 2 
0 0 1 0 0 0 0 0 
0 0 0 2 0 0 0 0 
1 2 3 2 3 0 3 0 
, 1
)
acting on the columns of the generator matrix as follows (in order):
(3, 6)(4, 7)(5, 8)(10, 13)(11, 14)(12, 17), 
(3, 10, 6, 13)(4, 11, 7, 14)(5, 12, 8, 17)(15, 16), 
(2, 12, 8, 5)(3, 4)(6, 13, 11, 16)(7, 14, 10, 15), 
(2, 6, 16, 12, 15, 7)(3, 10, 17, 11, 4, 5)(8, 14, 13), 
(1, 13, 6, 11)(2, 5, 14, 3)(4, 7, 15, 12)(8, 10), 
(1, 2, 12, 6, 8, 3, 13, 14, 5, 16, 4, 7, 11, 15, 10), 
(1, 12, 14, 13, 5, 3, 6, 17)(2, 10, 15, 4, 7, 11, 8, 16)
orbits: { 1, 11, 10, 17, 14, 4, 13, 6, 7, 3, 8, 15, 2, 12, 5, 16 }, { 9 }

code no       2:
================
1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0
2 2 2 1 1 1 0 0 0 1 0 0 0 0 0 0 0
3 2 1 2 1 0 1 0 0 0 1 0 0 0 0 0 0
3 1 2 1 2 0 0 1 0 0 0 1 0 0 0 0 0
3 0 0 3 3 1 1 1 0 0 0 0 1 0 0 0 0
0 1 0 2 1 3 2 1 0 0 0 0 0 1 0 0 0
3 2 1 3 2 3 2 1 0 0 0 0 0 0 1 0 0
0 0 3 3 1 2 3 1 0 0 0 0 0 0 0 1 0
2 3 1 1 2 2 3 1 0 0 0 0 0 0 0 0 1
the automorphism group has order 16320
and is strongly generated by the following 8 elements:
(
3 0 0 0 0 0 0 0 
0 3 0 0 0 0 0 0 
0 0 3 0 0 0 0 0 
0 0 0 3 0 0 0 0 
0 0 0 0 3 0 0 0 
1 1 1 3 3 3 0 0 
2 1 3 1 3 0 3 0 
2 3 1 3 1 0 0 3 
, 0
, 
2 0 0 0 0 0 0 0 
0 3 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 3 0 0 0 0 
2 0 0 2 2 1 1 1 
0 3 0 2 3 1 2 3 
0 0 3 3 2 1 3 2 
, 1
, 
3 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 
0 0 2 2 1 3 2 1 
1 2 3 2 3 0 3 0 
2 2 2 3 3 3 0 0 
0 0 0 0 0 0 2 0 
0 0 0 0 0 2 0 0 
0 0 3 0 0 0 0 0 
, 1
, 
2 0 0 0 0 0 0 0 
0 3 0 0 0 0 0 0 
0 0 0 0 0 0 1 0 
1 2 3 3 1 1 2 3 
0 0 0 0 0 1 0 0 
2 3 1 3 1 0 0 3 
3 2 1 3 2 3 2 1 
2 1 3 1 3 0 3 0 
, 0
, 
1 0 0 0 0 0 0 0 
0 0 0 3 0 0 0 0 
0 3 0 0 0 0 0 0 
0 0 0 0 3 0 0 0 
0 0 3 0 0 0 0 0 
0 0 0 0 0 0 0 1 
3 3 3 1 1 1 0 0 
2 0 0 2 2 1 1 1 
, 1
, 
3 3 3 2 2 2 0 0 
3 2 1 3 2 3 2 1 
2 1 3 1 3 0 3 0 
2 2 2 2 2 2 2 2 
0 0 0 0 0 0 0 2 
0 0 3 0 0 0 0 0 
0 3 0 0 0 0 0 0 
0 0 0 0 0 0 1 0 
, 0
, 
0 0 2 2 3 1 2 3 
0 0 3 0 0 0 0 0 
3 2 1 2 1 0 1 0 
2 1 3 2 1 2 1 3 
0 0 0 0 1 0 0 0 
1 2 3 2 3 0 0 2 
0 0 0 0 0 0 0 3 
0 1 0 2 1 3 2 1 
, 0
, 
3 2 1 1 3 3 2 1 
2 2 2 2 2 2 2 2 
0 0 3 3 2 1 3 2 
0 3 0 0 0 0 0 0 
2 0 0 2 2 1 1 1 
0 3 0 2 3 1 2 3 
0 0 0 0 0 0 0 3 
3 0 0 0 0 0 0 0 
, 1
)
acting on the columns of the generator matrix as follows (in order):
(6, 10)(7, 11)(8, 12)(9, 13)(14, 15)(16, 17), 
(4, 5)(6, 9, 10, 13)(7, 15, 11, 14)(8, 17, 12, 16), 
(3, 8, 12, 16)(4, 13, 15, 11)(5, 14, 9, 10)(6, 7), 
(3, 10, 13, 12, 6, 5, 16, 14, 9, 17, 4, 11, 8, 15, 7), 
(2, 3, 5, 4)(6, 11, 13, 8)(7, 9, 12, 10)(14, 15), 
(1, 13, 11, 3, 6, 15, 2, 7, 8, 5, 14, 9, 4, 12, 10), 
(1, 10, 12, 6, 13, 16)(2, 14, 8, 7, 11, 3)(4, 9, 15), 
(1, 8, 7, 10, 11, 14, 6, 17)(2, 4, 12, 16, 3, 13, 5, 9)
orbits: { 1, 10, 16, 17, 6, 9, 3, 12, 7, 5, 13, 8, 14, 4, 2, 11, 15 }