the 1 isometry classes of irreducible [16,5,8]_2 codes are:

code no       1:
================
1 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0
1 1 1 1 0 0 0 1 1 1 0 0 1 0 0 0
1 1 0 0 1 1 0 1 1 0 1 0 0 1 0 0
1 0 1 0 1 0 1 1 0 1 1 0 0 0 1 0
1 0 0 1 0 1 1 0 1 1 1 0 0 0 0 1
the automorphism group has order 322560
and is strongly generated by the following 13 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 
1 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 
1 0 0 1 0 1 1 0 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 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 
1 1 1 1 0 0 0 1 1 1 0 
1 1 0 0 1 1 0 1 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 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 
1 0 1 0 1 0 1 1 0 1 1 
1 0 0 1 0 1 1 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 
, 
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 0 0 1 0 
1 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 
1 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 
, 
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 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 
, 
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 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 
1 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 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 1 0 0 0 0 0 0 0 
1 0 1 0 1 0 1 1 0 1 1 
1 0 0 1 0 1 1 0 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 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 
, 
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 
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 
1 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 0 0 0 0 0 0 0 0 0 1 
1 1 1 1 1 1 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 
1 0 0 1 0 1 1 0 1 1 1 
1 0 1 0 1 0 1 1 0 1 1 
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 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 
1 1 1 1 0 0 0 1 1 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 0 0 0 1 1 1 0 
1 1 1 1 1 1 1 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 0 0 0 0 0 0 1 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 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 
, 
1 0 0 0 0 0 0 0 0 0 0 
1 0 0 1 0 1 1 0 1 1 1 
0 0 0 0 0 0 0 1 0 0 0 
1 1 1 1 1 1 1 0 0 0 0 
0 0 1 0 0 0 0 0 0 0 0 
1 1 0 0 1 1 0 1 1 0 1 
0 0 0 0 0 0 0 0 0 1 0 
0 0 0 1 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 
1 1 1 1 0 0 0 1 1 1 0 
0 1 0 0 0 0 0 0 0 0 0 
, 
1 0 1 0 1 0 1 1 0 1 1 
1 1 1 1 0 0 0 1 1 1 0 
0 0 1 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 0 1 0 0 0 
1 1 0 0 1 1 0 1 1 0 1 
0 0 0 0 1 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 0 0 1 
0 0 0 0 0 0 1 0 0 0 0 
, 
1 0 0 1 0 1 1 0 1 1 1 
0 0 0 0 0 1 0 0 0 0 0 
1 1 1 1 1 1 1 0 0 0 0 
1 1 0 0 1 1 0 1 1 0 1 
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 1 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 
1 1 1 1 0 0 0 1 1 1 0 
0 0 0 0 1 0 0 0 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(8, 13)(9, 10)(11, 16)(14, 15), 
(8, 9)(10, 13)(11, 14)(15, 16), 
(8, 15)(9, 16)(10, 11)(13, 14), 
(5, 10)(6, 13)(7, 8)(9, 12), 
(5, 8)(6, 9)(7, 10)(12, 13), 
(5, 13)(6, 10)(7, 9)(8, 12), 
(5, 15)(6, 16)(7, 11)(12, 14), 
(3, 5, 9)(4, 6, 8)(7, 14, 13)(10, 12, 11), 
(3, 16)(4, 15)(5, 8)(6, 9)(7, 12)(10, 13), 
(2, 5, 15, 13)(3, 8, 14, 12)(4, 11)(6, 10), 
(2, 11, 9, 15, 14, 6, 12, 4, 8, 3, 5, 13, 10, 7, 16), 
(1, 8, 5, 7, 11, 10, 15)(2, 12, 4, 14, 6, 9, 13), 
(1, 7, 16)(2, 13, 10, 12, 3, 6)(4, 8, 5, 11, 15, 14)
orbits: { 1, 15, 16, 14, 8, 5, 4, 9, 10, 11, 6, 3, 7, 13, 12, 2 }