the 1 isometry classes of irreducible [16,11,4]_2 codes are:

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