the 1 isometry classes of irreducible [17,13,5]_16 codes are:

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