the 2 isometry classes of irreducible [18,15,3]_4 codes are:

code no       1:
================
1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
3 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
2 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
3 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
2 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
3 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
0 2 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
1 2 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 576
and is strongly generated by the following 7 elements:
(
2 0 0 
0 3 0 
0 0 1 
, 1
, 
3 0 0 
0 1 0 
0 0 1 
, 0
, 
2 0 0 
0 3 0 
0 3 3 
, 1
, 
1 0 0 
0 1 0 
0 1 3 
, 0
, 
1 0 0 
1 2 2 
3 3 2 
, 0
, 
2 0 0 
1 0 3 
3 2 1 
, 0
, 
0 1 2 
3 3 2 
3 2 1 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(4, 17)(5, 6)(8, 10)(11, 14)(12, 16)(13, 15), 
(4, 12, 13)(5, 6, 7)(8, 9, 10)(15, 16, 17), 
(3, 11)(4, 9)(5, 6)(8, 12)(10, 13)(15, 16), 
(3, 11, 14)(4, 17, 9)(8, 13, 16)(10, 12, 15), 
(2, 12, 6, 11, 5, 13)(3, 15, 8, 14, 10, 16)(4, 7)(9, 17), 
(2, 17, 3, 7, 14, 9)(4, 11)(5, 16, 10, 6, 15, 8)(12, 13), 
(1, 18)(2, 12, 16)(3, 4, 8, 7, 10, 17)(5, 15, 14, 11, 13, 6)
orbits: { 1, 18 }, { 2, 13, 9, 16, 15, 12, 10, 8, 5, 11, 4, 17, 14, 3, 6, 7 }

code no       2:
================
1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
3 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
2 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
3 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
2 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
3 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
0 2 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
1 2 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 108
and is strongly generated by the following 5 elements:
(
2 0 0 
0 2 0 
2 2 2 
, 1
, 
1 0 0 
2 0 3 
1 3 3 
, 0
, 
3 0 0 
0 2 2 
0 0 2 
, 1
, 
0 3 1 
3 3 0 
3 2 0 
, 0
, 
3 2 2 
3 0 3 
2 2 2 
, 1
)
acting on the columns of the generator matrix as follows (in order):
(3, 4)(6, 7)(8, 11)(9, 12)(10, 13)(14, 15)(17, 18), 
(2, 13, 10)(3, 6, 12)(4, 9, 7)(5, 11, 8)(14, 16, 15), 
(2, 11)(4, 7)(5, 13)(6, 12)(8, 10)(15, 16), 
(1, 17)(2, 11, 13, 8, 10, 5)(3, 12, 6)(4, 16, 9, 15, 7, 14), 
(1, 8, 2, 17, 5, 13)(3, 15, 14, 12, 9, 4)(7, 16)(10, 18, 11)
orbits: { 1, 17, 13, 18, 2, 10, 5, 11, 8 }, { 3, 4, 12, 6, 7, 14, 9, 15, 16 }