the 3 isometry classes of irreducible [17,6,7]_2 codes are:

code no       1:
================
1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0
1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0
1 1 1 0 0 0 1 1 1 0 0 0 0 1 0 0 0
1 0 0 1 1 0 1 1 0 1 0 0 0 0 1 0 0
0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 1 0
0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 1
the automorphism group has order 1440
and is strongly generated by the following 8 elements:
(
1 0 0 0 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 
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 1 0 0 0 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 0 0 0 1 0 0 
0 0 0 0 0 0 0 0 0 1 0 
1 1 1 1 1 1 1 1 1 1 1 
, 
1 0 0 0 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 
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 1 0 0 0 0 0 
0 0 1 0 1 1 0 1 1 1 0 
0 1 0 1 0 1 1 0 1 1 0 
1 0 0 1 1 0 1 1 0 1 0 
1 1 1 0 0 0 1 1 1 0 0 
0 0 0 0 0 0 0 0 0 0 1 
, 
1 0 0 0 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 
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 0 0 0 1 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 0 0 0 1 0 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 1 
, 
1 0 0 0 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 
0 0 1 0 1 1 0 1 1 1 0 
0 1 0 1 0 1 1 0 1 1 0 
1 0 0 1 1 0 1 1 0 1 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 0 0 0 1 0 0 0 0 0 
1 1 1 0 0 0 1 1 1 0 0 
1 1 1 1 1 1 1 1 1 1 1 
, 
1 0 0 0 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 1 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 0 0 0 0 0 0 0 1 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 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 0 0 1 
, 
1 0 0 0 0 0 0 0 0 0 0 
0 1 0 1 0 1 1 0 1 1 0 
0 0 1 0 1 1 0 1 1 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 1 1 0 1 1 0 1 0 
0 0 0 0 1 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 
1 1 1 0 0 0 1 1 1 0 0 
0 0 0 0 0 1 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 
, 
0 1 0 1 0 1 1 0 1 1 0 
1 1 1 0 0 0 1 1 1 0 0 
0 0 0 0 1 0 0 0 0 0 0 
1 1 1 1 1 1 0 0 0 0 0 
0 0 0 0 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 0 0 1 0 
1 0 0 1 1 0 1 1 0 1 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 0 0 1 0 0 
1 1 1 1 1 1 1 1 1 1 1 
, 
0 1 0 0 0 0 0 0 0 0 0 
1 0 0 0 0 0 0 0 0 0 0 
0 0 1 0 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 0 1 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 0 1 0 0 0 0 0 
0 0 0 0 1 0 0 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 1 
)
acting on the columns of the generator matrix as follows (in order):
(11, 12), 
(7, 17)(8, 16)(9, 15)(10, 14), 
(4, 7)(5, 8)(6, 9)(13, 14), 
(4, 7, 17)(5, 8, 16)(6, 9, 15)(10, 13, 14)(11, 12), 
(2, 7)(3, 8)(6, 10)(13, 15), 
(2, 5, 7, 16)(3, 4, 8, 17)(6, 10, 13, 15)(9, 14), 
(1, 16)(2, 13, 4, 15, 7, 14)(3, 8, 5)(6, 9, 10)(11, 12), 
(1, 2)(4, 7)(5, 9)(6, 8)(13, 14)(15, 16)
orbits: { 1, 16, 2, 8, 7, 15, 14, 5, 3, 4, 6, 17, 9, 13, 10 }, { 11, 12 }

code no       2:
================
1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0
1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0
1 1 1 0 0 0 1 1 1 0 0 0 0 1 0 0 0
1 0 0 1 1 0 1 1 0 1 0 0 0 0 1 0 0
0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 1 0
0 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 1
the automorphism group has order 120
and is strongly generated by the following 6 elements:
(
1 0 0 0 0 0 0 0 0 0 0 
1 0 0 1 1 0 1 1 0 1 0 
0 0 0 0 0 0 0 0 0 1 0 
0 0 0 0 0 0 0 0 1 0 0 
1 1 1 0 0 0 1 1 1 0 0 
1 1 1 1 1 1 0 0 0 0 0 
0 0 0 0 0 0 0 1 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 1 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 
, 
1 0 0 0 0 0 0 0 0 0 0 
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 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 
1 1 1 1 1 1 0 0 0 0 0 
0 0 1 1 0 1 1 1 0 0 1 
1 1 1 1 1 1 1 1 1 1 1 
1 0 0 1 1 0 1 1 0 1 0 
0 0 0 0 0 0 0 0 0 1 0 
0 1 0 1 0 1 1 0 1 1 0 
, 
1 0 0 0 0 0 0 0 0 0 0 
1 1 1 1 1 1 1 1 1 1 1 
0 0 1 0 0 0 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 1 0 1 1 0 1 1 0 
1 0 0 1 1 0 1 1 0 1 0 
0 0 0 1 0 0 0 0 0 0 0 
0 0 1 1 0 1 1 1 0 0 1 
0 0 0 0 0 0 0 0 0 1 0 
1 1 1 1 1 1 0 0 0 0 0 
, 
0 1 0 1 0 1 1 0 1 1 0 
1 0 0 1 1 0 1 1 0 1 0 
0 0 1 0 0 0 0 0 0 0 0 
1 1 1 1 1 1 0 0 0 0 0 
0 0 0 0 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 
1 1 1 0 0 0 1 1 1 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 0 0 0 0 0 0 1 0 
0 0 0 0 0 0 0 0 0 0 1 
, 
1 1 1 1 1 1 0 0 0 0 0 
1 1 1 0 0 0 1 1 1 0 0 
0 0 0 0 0 0 0 0 0 1 0 
1 0 0 1 1 0 1 1 0 1 0 
0 0 0 0 0 0 0 0 1 0 0 
0 0 0 0 0 1 0 0 0 0 0 
0 1 0 1 0 1 1 0 1 1 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 1 0 0 0 0 0 0 0 0 
1 1 1 1 1 1 1 1 1 1 1 
, 
0 0 1 1 0 1 1 1 0 0 1 
1 1 1 0 0 0 1 1 1 0 0 
0 0 1 0 0 0 0 0 0 0 0 
1 1 1 1 1 1 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 
0 0 0 0 0 0 0 0 1 0 0 
1 0 0 1 1 0 1 1 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 0 0 0 0 0 1 0 
0 0 0 0 0 0 0 1 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(2, 15)(3, 10)(4, 9)(5, 14)(6, 13)(7, 8)(12, 17), 
(2, 4)(6, 13)(7, 17)(8, 12)(9, 15)(11, 16), 
(2, 12)(4, 8)(6, 16)(7, 15)(9, 17)(11, 13), 
(1, 16)(2, 15)(4, 13)(5, 8)(6, 9)(7, 14), 
(1, 13)(2, 14)(3, 10)(4, 15)(5, 9)(7, 16)(11, 12), 
(1, 9, 6, 16, 17)(2, 15, 7, 12, 14)(4, 8, 11, 5, 13)
orbits: { 1, 16, 13, 17, 11, 6, 7, 4, 5, 12, 9, 8, 15, 14, 2 }, { 3, 10 }

code no       3:
================
1 1 1 1 1 1 0 0 0 0 0 1 0 0 0 0 0
1 1 1 0 0 0 1 1 1 0 0 0 1 0 0 0 0
1 0 0 1 1 0 1 1 0 1 0 0 0 1 0 0 0
1 0 0 1 0 1 1 0 1 0 1 0 0 0 1 0 0
0 1 0 1 1 1 1 0 0 1 1 0 0 0 0 1 0
0 0 1 1 0 0 1 1 1 1 1 0 0 0 0 0 1
the automorphism group has order 11520
and is strongly generated by the following 8 elements:
(
1 0 0 0 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 
0 0 0 1 0 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 
1 1 1 1 1 1 0 0 0 0 0 
0 0 0 0 0 0 0 1 0 0 0 
0 0 0 0 0 0 1 0 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 
0 0 0 0 0 0 0 0 0 1 0 
0 0 1 1 0 0 1 1 1 1 1 
, 
1 0 0 0 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 
0 0 0 1 0 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 
0 0 0 0 0 0 1 0 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 
0 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 1 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 1 0 0 0 0 0 0 0 0 
1 1 1 1 1 1 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 
1 1 1 0 0 0 1 1 1 0 0 
0 0 0 0 0 0 0 0 1 0 0 
0 0 0 0 0 0 0 1 0 0 0 
1 0 0 1 1 0 1 1 0 1 0 
1 0 0 1 0 1 1 0 1 0 1 
, 
1 0 0 0 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 
0 0 0 0 0 0 1 0 0 0 0 
0 0 0 0 0 0 0 0 1 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 0 1 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 
1 0 0 1 0 1 1 0 1 0 1 
1 0 0 1 1 0 1 1 0 1 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 1 0 0 0 0 0 0 0 0 
0 0 0 0 0 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 0 
0 0 0 1 0 0 0 0 0 0 0 
1 1 1 1 1 1 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 
0 1 0 1 1 1 1 0 0 1 1 
1 0 0 1 0 1 1 0 1 0 1 
, 
1 0 0 0 0 0 0 0 0 0 0 
0 1 0 0 0 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 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 1 0 1 1 0 1 0 
0 0 0 0 0 0 0 1 0 0 0 
0 1 0 1 1 1 1 0 0 1 1 
0 0 0 0 0 0 0 0 0 1 0 
1 1 1 0 0 0 1 1 1 0 0 
, 
1 0 0 0 0 0 0 0 0 0 0 
1 0 0 1 0 1 1 0 1 0 1 
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 1 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 
1 1 1 1 1 1 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 
1 1 1 0 0 0 1 1 1 0 0 
0 0 1 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 1 0 
, 
1 0 0 0 0 0 0 0 0 0 0 
0 0 1 1 0 0 1 1 1 1 1 
0 1 0 0 0 0 0 0 0 0 0 
1 1 1 1 1 1 0 0 0 0 0 
0 0 0 0 0 0 1 0 0 0 0 
1 0 0 1 0 1 1 0 1 0 1 
0 0 0 0 0 0 0 0 0 0 1 
0 0 0 0 0 0 0 0 0 1 0 
1 1 1 0 0 0 1 1 1 0 0 
0 1 0 1 1 1 1 0 0 1 1 
0 0 0 0 0 0 0 1 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(6, 12)(7, 8)(11, 17)(15, 16), 
(5, 6)(8, 9)(10, 11)(14, 15), 
(4, 12)(5, 6)(7, 13)(8, 9)(10, 14)(11, 15), 
(4, 7)(5, 9)(6, 8)(10, 15)(11, 14)(12, 13), 
(4, 7, 6, 9)(5, 13, 12, 8)(10, 17, 14, 16)(11, 15), 
(3, 6)(7, 14)(9, 16)(11, 13), 
(2, 14, 15)(3, 10, 11)(4, 5, 8, 13, 9, 6)(7, 12), 
(2, 3, 14, 12, 4, 13, 9, 17)(5, 15, 6, 16, 10, 8, 11, 7)
orbits: { 1 }, { 2, 15, 17, 16, 14, 11, 10, 5, 9, 6, 7, 3, 13, 8, 4, 12 }