the 5 isometry classes of irreducible [16,5,7]_2 codes are:

code no       1:
================
1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0
1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0
1 1 1 0 0 0 1 1 1 0 0 0 0 1 0 0
1 0 0 1 1 0 1 1 0 1 0 0 0 0 1 0
0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 1
the automorphism group has order 96
and is strongly generated by the following 5 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 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 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 
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 
, 
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 
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 
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 0 1 0 0 0 0 0 0 0 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), 
(4, 7)(5, 8)(6, 9)(13, 14), 
(2, 7)(3, 8)(6, 10)(11, 12)(13, 15), 
(1, 2)(4, 7)(5, 9)(6, 8)(13, 14)(15, 16), 
(1, 14, 2, 13)(3, 10)(4, 15, 7, 16)(5, 6, 9, 8)
orbits: { 1, 2, 13, 7, 14, 15, 4, 16 }, { 3, 8, 10, 5, 6, 9 }, { 11, 12 }

code no       2:
================
1 1 1 1 1 1 0 0 0 0 0 1 0 0 0 0
1 1 1 0 0 0 1 1 1 0 0 0 1 0 0 0
1 0 0 1 1 0 1 1 0 1 0 0 0 1 0 0
0 1 0 1 0 1 1 0 1 1 0 0 0 0 1 0
0 1 1 1 1 0 1 1 0 0 1 0 0 0 0 1
the automorphism group has order 192
and is strongly generated by the following 7 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 
0 1 1 1 1 0 1 1 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 1 0 0 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 0 0 1 0 0 0 
0 0 0 0 0 0 1 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 
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 1 0 0 0 0 0 
1 1 1 1 1 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 0 0 0 1 1 1 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 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 0 1 0 0 0 
0 0 0 0 0 0 1 0 0 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 1 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 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 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 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 
1 1 1 0 0 0 1 1 1 0 0 
1 0 0 1 1 0 1 1 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 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 0 0 1 0 0 0 0 0 0 
1 0 0 1 1 0 1 1 0 1 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 1 0 0 
1 1 1 1 1 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 
1 1 1 0 0 0 1 1 1 0 0 
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 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 1 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 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(11, 16), 
(4, 5)(6, 12)(7, 8)(9, 13), 
(4, 6)(5, 12)(7, 9)(8, 13), 
(4, 8)(5, 7)(6, 13)(9, 12), 
(2, 3)(4, 5)(9, 13)(10, 14), 
(2, 8)(3, 7)(6, 14)(10, 12), 
(2, 13)(3, 9)(4, 14)(5, 10)
orbits: { 1 }, { 2, 3, 8, 13, 7, 9, 4, 6, 5, 12, 14, 10 }, { 11, 16 }, { 15 }

code no       3:
================
1 1 1 1 1 1 0 0 0 0 0 1 0 0 0 0
1 1 1 0 0 0 1 1 1 0 0 0 1 0 0 0
1 0 0 1 1 0 1 1 0 1 0 0 0 1 0 0
0 1 0 1 0 1 1 0 1 1 0 0 0 0 1 0
0 0 1 0 1 1 0 1 1 1 1 0 0 0 0 1
the automorphism group has order 2688
and is strongly generated by the following 7 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 
0 0 1 0 1 1 0 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 0 0 0 0 1 0 0 0 
0 0 0 0 0 0 1 0 0 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 1 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 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 0 0 1 0 0 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 0 0 1 0 0 0 
0 0 0 0 0 0 1 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 
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 0 0 1 0 0 
1 1 1 0 0 0 1 1 1 0 0 
0 0 0 0 0 0 1 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 
1 1 1 1 1 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 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 
1 1 1 1 1 1 0 0 0 0 0 
0 0 0 0 0 1 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 
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 
0 0 0 0 0 0 0 1 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 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 1 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 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 0 0 0 0 1 
, 
1 1 1 1 1 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 0 0 
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 0 0 0 0 0 0 1 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 1 0 1 0 1 1 0 1 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, 16), 
(4, 8)(5, 7)(6, 13)(9, 12), 
(4, 5)(6, 12)(7, 8)(9, 13), 
(4, 9)(5, 13)(6, 7)(8, 12), 
(2, 13, 12)(3, 9, 6)(4, 7, 14)(5, 8, 10), 
(2, 12, 4)(3, 6, 5)(7, 13, 14)(8, 9, 10), 
(1, 3, 8, 14, 5, 13, 12)(2, 9, 4, 7, 15, 10, 6)
orbits: { 1, 12, 9, 6, 8, 13, 2, 4, 3, 7, 10, 5, 14, 15 }, { 11, 16 }

code no       4:
================
1 1 1 1 1 1 0 0 0 0 0 1 0 0 0 0
1 1 1 0 0 0 1 1 1 0 0 0 1 0 0 0
1 0 0 1 1 0 1 1 0 1 0 0 0 1 0 0
0 1 1 1 1 0 1 1 0 0 1 0 0 0 1 0
0 1 0 1 0 1 1 0 1 1 1 0 0 0 0 1
the automorphism group has order 1344
and is strongly generated by the following 7 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 0 0 0 1 0 
1 0 0 1 1 0 1 1 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 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 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 
1 0 0 1 1 0 1 1 0 1 0 
0 0 0 0 0 0 0 0 0 1 0 
0 1 1 1 1 0 1 1 0 0 1 
0 0 0 0 0 0 0 1 0 0 0 
1 1 1 0 0 0 1 1 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 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 0 1 0 0 
1 1 1 0 0 0 1 1 1 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 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 0 0 1 
0 1 1 1 1 0 1 1 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 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 
1 1 1 1 1 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 1 0 0 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 0 0 1 0 0 0 
0 0 0 0 0 0 1 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 
0 0 0 0 0 0 0 0 0 0 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 
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 1 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 1 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 1 0 
0 1 1 1 1 0 1 1 0 0 1 
, 
1 0 0 0 0 0 0 0 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 0 0 0 0 0 0 1 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 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 1 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(7, 10)(8, 14)(9, 11)(13, 15), 
(7, 14)(8, 10)(9, 15)(11, 13), 
(7, 9)(8, 13)(10, 11)(14, 15), 
(4, 14, 12, 11)(5, 10, 6, 15)(7, 13)(8, 9), 
(4, 5)(6, 12)(7, 8)(9, 13), 
(2, 3)(4, 9, 5, 13)(6, 8, 12, 7)(11, 15), 
(2, 10)(3, 14)(4, 9)(5, 13)
orbits: { 1 }, { 2, 3, 10, 14, 7, 8, 11, 5, 15, 4, 9, 13, 12, 6 }, { 16 }

code no       5:
================
1 1 1 1 1 1 0 0 0 0 0 1 0 0 0 0
1 1 1 0 0 0 1 1 1 0 0 0 1 0 0 0
1 0 0 1 1 0 1 1 0 1 0 0 0 1 0 0
1 0 0 1 0 1 1 0 1 0 1 0 0 0 1 0
0 1 0 1 1 1 1 0 0 1 1 0 0 0 0 1
the automorphism group has order 720
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 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 0 0 0 1 1 1 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 1 1 1 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 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 
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 
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 0 0 0 0 0 0 1 0 0 
1 1 1 0 0 0 1 1 1 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 1 0 1 1 0 1 0 1 
0 0 0 0 1 0 0 0 0 0 0 
0 1 0 1 1 1 1 0 0 1 1 
0 0 0 0 0 0 0 0 0 0 1 
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 
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 0 1 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 
1 1 1 1 1 1 0 0 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 
0 1 0 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 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 1 0 0 
1 1 1 0 0 0 1 1 1 0 0 
0 0 0 0 0 0 1 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 
1 1 1 1 1 1 0 0 0 0 0 
0 0 0 1 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 0 1 
, 
1 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 
1 0 0 1 0 1 1 0 1 0 1 
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 0 0 1 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 1 0 
0 1 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 0 0 1 1 
0 0 0 0 0 0 0 0 0 1 0 
0 0 0 0 1 0 0 0 0 0 0 
1 0 0 1 0 1 1 0 1 0 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 0 0 0 0 1 
0 0 1 0 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 
)
acting on the columns of the generator matrix as follows (in order):
(5, 6)(8, 9)(10, 11)(14, 15), 
(4, 13)(5, 8)(6, 9)(7, 12)(10, 11)(14, 15), 
(4, 7)(5, 8)(6, 9)(10, 14)(11, 15)(12, 13), 
(3, 6, 16, 9)(4, 11, 10, 13)(5, 8)(7, 12, 14, 15), 
(2, 10)(3, 14)(6, 7)(8, 12), 
(2, 3)(4, 9)(5, 13)(6, 7)(8, 12)(10, 14), 
(2, 11)(3, 15)(4, 13)(5, 12)(6, 8)(7, 9), 
(2, 6, 11, 8, 14, 16)(3, 9, 12, 7, 13, 10)(4, 15, 5)
orbits: { 1 }, { 2, 10, 3, 11, 16, 14, 13, 9, 15, 4, 6, 12, 8, 5, 7 }