the 3 isometry classes of irreducible [5,2,4]_16 codes are:

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

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

code no       3:
================
1 1 1 1 0
11 10 1 0 1
the automorphism group has order 240
and is strongly generated by the following 7 elements:
(
3 0 0 
0 3 0 
0 0 3 
, 2
, 
15 0 0 
0 2 0 
0 0 13 
, 1
, 
6 0 0 
0 6 0 
6 6 6 
, 1
, 
6 0 0 
6 6 6 
0 6 0 
, 2
, 
0 0 6 
0 6 0 
6 0 0 
, 1
, 
11 11 11 
0 0 11 
11 0 0 
, 1
, 
13 2 15 
2 0 0 
15 15 15 
, 0
)
acting on the columns of the generator matrix as follows (in order):
id, 
(4, 5), 
(3, 4), 
(2, 3, 4), 
(1, 3), 
(1, 3, 2, 4), 
(1, 2, 4, 3, 5)
orbits: { 1, 3, 4, 5, 2 }