the 22 isometry classes of irreducible [6,3,4]_16 codes are:

code no       1:
================
1 1 1 1 0 0
3 2 1 0 1 0
2 3 1 0 0 1
the automorphism group has order 24
and is strongly generated by the following 5 elements:
(
10 0 0 
0 10 0 
13 7 10 
, 0
, 
13 0 0 
0 13 0 
13 13 13 
, 0
, 
4 4 4 
0 0 4 
0 4 0 
, 0
, 
0 14 0 
14 0 0 
14 14 14 
, 0
, 
11 2 9 
2 11 9 
0 9 0 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(3, 6)(4, 5), 
(3, 4)(5, 6), 
(1, 4)(2, 3), 
(1, 2)(3, 4), 
(1, 4, 6)(2, 3, 5)
orbits: { 1, 4, 2, 6, 5, 3 }

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

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

code no       4:
================
1 1 1 1 0 0
3 2 1 0 1 0
6 3 1 0 0 1
the automorphism group has order 1
and is strongly generated by the following 0 elements:
(
)
acting on the columns of the generator matrix as follows (in order):
orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }

code no       5:
================
1 1 1 1 0 0
3 2 1 0 1 0
7 3 1 0 0 1
the automorphism group has order 1
and is strongly generated by the following 0 elements:
(
)
acting on the columns of the generator matrix as follows (in order):
orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }

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

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

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

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

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

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

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

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

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

code no      15:
================
1 1 1 1 0 0
3 2 1 0 1 0
8 9 1 0 0 1
the automorphism group has order 48
and is strongly generated by the following 5 elements:
(
13 0 0 
0 13 0 
0 0 13 
, 2
, 
15 0 0 
15 15 15 
0 0 15 
, 2
, 
6 0 0 
3 6 5 
0 0 6 
, 2
, 
0 14 0 
14 0 0 
14 14 14 
, 0
, 
11 5 14 
5 5 5 
14 5 11 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(5, 6), 
(2, 4), 
(2, 6, 4, 5), 
(1, 2)(3, 4), 
(1, 6, 3, 5)(2, 4)
orbits: { 1, 2, 5, 4, 6, 3 }

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

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

code no      18:
================
1 1 1 1 0 0
5 2 1 0 1 0
11 5 1 0 0 1
the automorphism group has order 12
and is strongly generated by the following 3 elements:
(
8 0 0 
12 1 5 
0 0 8 
, 2
, 
12 3 14 
0 0 2 
0 15 0 
, 2
, 
0 3 0 
6 0 0 
12 15 11 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(2, 6)(4, 5), 
(1, 5)(2, 3), 
(1, 2)(3, 5)(4, 6)
orbits: { 1, 5, 2, 4, 3, 6 }

code no      19:
================
1 1 1 1 0 0
5 2 1 0 1 0
12 5 1 0 0 1
the automorphism group has order 3
and is strongly generated by the following 1 elements:
(
9 13 10 
5 9 10 
12 0 0 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(1, 3, 5)(2, 4, 6)
orbits: { 1, 5, 3 }, { 2, 6, 4 }

code no      20:
================
1 1 1 1 0 0
5 2 1 0 1 0
2 8 1 0 0 1
the automorphism group has order 6
and is strongly generated by the following 2 elements:
(
0 0 2 
6 6 6 
12 2 6 
, 0
, 
9 4 6 
9 0 0 
0 4 0 
, 2
)
acting on the columns of the generator matrix as follows (in order):
(1, 6, 3)(2, 5, 4), 
(1, 2, 3, 4, 6, 5)
orbits: { 1, 3, 5, 6, 2, 4 }

code no      21:
================
1 1 1 1 0 0
5 2 1 0 1 0
9 15 1 0 0 1
the automorphism group has order 20
and is strongly generated by the following 2 elements:
(
5 0 0 
4 8 1 
0 9 0 
, 1
, 
0 0 2 
15 0 0 
7 8 10 
, 1
)
acting on the columns of the generator matrix as follows (in order):
(2, 3, 5, 6), 
(1, 2, 5, 3)
orbits: { 1, 3, 2, 5, 6 }, { 4 }

code no      22:
================
1 1 1 1 0 0
11 10 1 0 1 0
10 11 1 0 0 1
the automorphism group has order 1440
and is strongly generated by the following 11 elements:
(
3 0 0 
0 3 0 
0 0 3 
, 2
, 
11 0 0 
0 11 0 
0 0 11 
, 3
, 
15 0 0 
0 2 0 
0 0 13 
, 1
, 
14 0 0 
0 8 0 
0 0 6 
, 0
, 
6 0 0 
0 6 0 
6 6 6 
, 1
, 
6 0 0 
6 6 6 
0 6 0 
, 2
, 
9 0 0 
12 9 5 
0 12 0 
, 0
, 
10 0 0 
1 11 10 
11 1 10 
, 3
, 
0 0 6 
0 6 0 
6 0 0 
, 1
, 
13 2 15 
2 0 0 
15 15 15 
, 0
, 
12 5 9 
0 0 9 
9 9 9 
, 0
)
acting on the columns of the generator matrix as follows (in order):
id, 
(5, 6), 
(4, 5), 
(4, 5, 6), 
(3, 4), 
(2, 3, 4), 
(2, 3, 5), 
(2, 4, 6)(3, 5), 
(1, 3), 
(1, 2, 4, 3, 5), 
(1, 6)(2, 5, 4, 3)
orbits: { 1, 3, 5, 6, 4, 2 }