the 1 isometry classes of irreducible [17,13,4]_4 codes are:

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