the 1 isometry classes of irreducible [4,1,4]_16 codes are:

code no       1:
================
1 1 1 1
the automorphism group has order 96
and is strongly generated by the following 7 elements:
(
4 0 0 
0 4 0 
0 0 4 
, 3
, 
12 0 0 
0 12 0 
12 12 12 
, 0
, 
11 0 0 
0 0 11 
0 11 0 
, 2
, 
6 0 0 
6 6 6 
0 6 0 
, 3
, 
0 0 6 
0 6 0 
6 0 0 
, 2
, 
0 14 0 
0 0 14 
14 0 0 
, 1
, 
4 4 4 
0 0 4 
4 0 0 
, 1
)
acting on the columns of the generator matrix as follows (in order):
id, 
(3, 4), 
(2, 3), 
(2, 3, 4), 
(1, 3), 
(1, 3, 2), 
(1, 3, 2, 4)
orbits: { 1, 3, 2, 4 }