the 4 isometry classes of irreducible [5,2,4]_27 codes are:

code no       1:
================
1 1 1 2 0
3 2 1 0 2
the automorphism group has order 3
and is strongly generated by the following 1 elements:
(
24 0 0 
12 12 12 
0 24 0 
, 1
)
acting on the columns of the generator matrix as follows (in order):
(2, 3, 4)
orbits: { 1 }, { 2, 4, 3 }, { 5 }

code no       2:
================
1 1 1 2 0
4 3 1 0 2
the automorphism group has order 2
and is strongly generated by the following 1 elements:
(
12 12 12 
0 0 24 
0 24 0 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(1, 4)(2, 3)
orbits: { 1, 4 }, { 2, 3 }, { 5 }

code no       3:
================
1 1 1 2 0
7 3 1 0 2
the automorphism group has order 2
and is strongly generated by the following 1 elements:
(
0 26 0 
26 0 0 
13 13 13 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(1, 2)(3, 4)
orbits: { 1, 2 }, { 3, 4 }, { 5 }

code no       4:
================
1 1 1 2 0
17 3 1 0 2
the automorphism group has order 3
and is strongly generated by the following 1 elements:
(
16 1 24 
0 26 0 
11 0 0 
, 2
)
acting on the columns of the generator matrix as follows (in order):
(1, 3, 5)
orbits: { 1, 5, 3 }, { 2 }, { 4 }