the 1 isometry classes of irreducible [5,1,5]_16 codes are:

code no       1:
================
1 1 1 1 1
the automorphism group has order 480
and is strongly generated by the following 7 elements:
(
15 0 0 0 
0 15 0 0 
0 0 15 0 
0 0 0 15 
, 1
, 
13 0 0 0 
0 13 0 0 
0 0 13 0 
13 13 13 13 
, 1
, 
5 0 0 0 
0 5 0 0 
0 0 0 5 
0 0 5 0 
, 0
, 
14 0 0 0 
0 14 0 0 
14 14 14 14 
0 0 14 0 
, 1
, 
2 0 0 0 
0 0 2 0 
0 0 0 2 
0 2 0 0 
, 0
, 
0 0 0 7 
0 0 7 0 
0 7 0 0 
7 0 0 0 
, 1
, 
5 5 5 5 
5 0 0 0 
0 5 0 0 
0 0 0 5 
, 2
)
acting on the columns of the generator matrix as follows (in order):
id, 
(4, 5), 
(3, 4), 
(3, 4, 5), 
(2, 4, 3), 
(1, 4)(2, 3), 
(1, 2, 3, 5)
orbits: { 1, 4, 5, 3, 2 }