the 2 isometry classes of irreducible [18,15,4]_16 codes are:

code no       1:
================
1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 2 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
2 3 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
8 4 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
9 5 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
13 6 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
12 7 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
14 8 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
15 9 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
7 10 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
6 11 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
11 12 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
10 13 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
4 14 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
5 15 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 144
and is strongly generated by the following 6 elements:
(
1 0 0 
0 1 0 
1 1 1 
, 0
, 
13 0 0 
0 13 0 
7 5 13 
, 2
, 
3 0 0 
0 3 0 
11 1 3 
, 3
, 
15 12 2 
2 14 7 
5 10 13 
, 1
, 
10 7 2 
10 10 10 
0 13 0 
, 0
, 
5 5 5 
5 15 1 
5 8 9 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18), 
(3, 9, 4, 10)(5, 18, 6, 17)(7, 11, 8, 12)(13, 15, 14, 16), 
(3, 11, 10, 7, 4, 12, 9, 8)(5, 15, 17, 13, 6, 16, 18, 14), 
(1, 6, 15, 5, 17, 13, 14, 16)(2, 10, 8, 9, 3, 11, 12, 7), 
(1, 17, 18)(2, 3, 4)(5, 13, 15)(6, 16, 14)(7, 12, 10)(8, 9, 11), 
(1, 10, 14, 4)(2, 6, 12, 18)(3, 5, 7, 15)(8, 17, 9, 16)(11, 13)
orbits: { 1, 16, 18, 4, 15, 14, 6, 9, 17, 5, 12, 3, 7, 13, 10, 2, 8, 11 }

code no       2:
================
1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 2 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
5 3 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
2 4 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
12 5 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
14 6 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
10 7 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
11 8 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
13 9 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
9 10 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
6 11 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
8 12 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
4 13 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
15 14 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
7 15 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 16320
and is strongly generated by the following 6 elements:
(
5 0 0 
0 15 0 
0 0 8 
, 2
, 
4 0 0 
0 1 0 
0 0 14 
, 1
, 
5 0 0 
0 8 0 
13 12 7 
, 3
, 
9 0 0 
0 10 0 
9 10 12 
, 1
, 
4 0 0 
7 15 10 
4 11 7 
, 2
, 
12 2 14 
2 13 4 
1 2 12 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(4, 6)(7, 14)(8, 11)(9, 12)(10, 13)(15, 17), 
(4, 17, 6, 15)(7, 8, 14, 11)(9, 10, 12, 13)(16, 18), 
(3, 16)(4, 7, 6, 14)(8, 13, 11, 10)(9, 15, 12, 17), 
(3, 4, 11, 10)(6, 14, 16, 8)(7, 13)(9, 12, 17, 18), 
(2, 6, 16, 10, 3, 15)(4, 14, 13, 12, 17, 8)(7, 11, 9), 
(1, 7, 3, 12, 17)(2, 16, 6, 14, 8)(4, 11, 15, 13, 9)
orbits: { 1, 17, 15, 4, 12, 6, 9, 3, 11, 14, 8, 10, 13, 7, 2, 16, 18 }, { 5 }