the 2 isometry classes of irreducible [16,7,8]_4 codes are:

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

code no       2:
================
1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0
3 2 2 2 1 1 1 0 0 0 1 0 0 0 0 0
2 3 2 1 2 1 0 1 0 0 0 1 0 0 0 0
2 2 3 1 1 2 0 0 1 0 0 0 1 0 0 0
0 1 2 3 2 0 2 1 1 0 0 0 0 1 0 0
1 0 2 2 3 0 1 2 1 0 0 0 0 0 1 0
3 0 3 0 1 1 3 2 1 0 0 0 0 0 0 1
the automorphism group has order 960
and is strongly generated by the following 6 elements:
(
1 0 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 0 
1 1 1 1 1 1 1 1 1 
2 1 1 1 3 3 3 0 0 
1 2 1 3 1 3 0 3 0 
0 0 0 0 0 0 0 0 1 
3 0 1 1 2 0 3 1 3 
0 3 1 2 1 0 1 3 3 
0 0 0 0 0 1 0 0 0 
, 0
, 
2 0 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 0 
0 0 0 0 0 0 2 0 0 
0 1 3 2 3 0 3 1 1 
0 0 0 0 0 3 0 0 0 
3 2 3 1 3 1 0 1 0 
2 2 2 2 2 2 2 2 2 
0 0 0 3 0 0 0 0 0 
0 0 0 0 3 0 0 0 0 
, 1
, 
3 0 0 0 0 0 0 0 0 
2 2 1 3 3 2 0 0 3 
0 0 0 0 3 0 0 0 0 
1 0 3 3 2 0 1 3 1 
3 3 3 3 3 3 3 3 3 
0 0 0 0 0 0 0 2 0 
0 0 0 3 0 0 0 0 0 
0 0 0 0 0 0 0 0 2 
0 3 2 1 2 0 2 3 3 
, 1
, 
2 0 0 0 0 0 0 0 0 
3 0 1 1 2 0 3 1 3 
0 0 0 0 0 0 1 0 0 
1 2 1 3 1 3 0 3 0 
3 3 1 2 2 3 0 0 2 
0 3 1 2 1 0 1 3 3 
0 0 3 0 0 0 0 0 0 
1 0 1 0 2 2 1 3 2 
0 0 0 0 0 0 0 0 2 
, 0
, 
2 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 
2 0 2 0 3 3 2 1 3 
0 2 0 0 0 0 0 0 0 
1 0 2 2 3 0 1 2 1 
3 3 1 2 2 3 0 0 2 
0 0 0 0 0 0 0 0 2 
0 0 0 0 3 0 0 0 0 
2 3 2 1 2 1 0 1 0 
, 0
, 
0 0 0 0 0 2 0 0 0 
3 2 3 1 3 1 0 1 0 
1 0 0 0 0 0 0 0 0 
0 0 2 0 0 0 0 0 0 
0 0 0 0 0 0 0 2 0 
0 0 0 3 0 0 0 0 0 
3 3 2 1 1 3 0 0 1 
0 1 0 0 0 0 0 0 0 
0 0 0 0 0 0 1 0 0 
, 1
)
acting on the columns of the generator matrix as follows (in order):
(3, 10)(4, 11)(5, 12)(6, 9)(7, 15)(8, 14), 
(3, 15, 10, 7)(4, 8, 11, 14)(5, 9, 12, 6)(13, 16), 
(2, 13)(3, 12, 10, 5)(4, 7, 11, 15)(6, 14, 9, 8), 
(2, 15)(3, 7)(4, 12)(5, 13)(6, 14)(8, 16), 
(2, 4, 16, 3, 13, 6)(5, 8, 15)(7, 11, 14, 10, 12, 9), 
(1, 3, 4, 6)(2, 8, 5, 12)(7, 9, 11, 13)(10, 15)
orbits: { 1, 6, 9, 12, 8, 14, 13, 4, 5, 7, 3, 10, 16, 2, 11, 15 }