the 1 isometry classes of irreducible [10,7,4]_8 codes are:

code no       1:
================
1 1 1 1 0 0 0 0 0 0
3 2 1 0 1 0 0 0 0 0
5 3 1 0 0 1 0 0 0 0
2 4 1 0 0 0 1 0 0 0
7 5 1 0 0 0 0 1 0 0
4 6 1 0 0 0 0 0 1 0
6 7 1 0 0 0 0 0 0 1
the automorphism group has order 1512
and is strongly generated by the following 7 elements:
(
3 0 0 
0 2 0 
0 0 1 
, 2
, 
1 0 0 
0 1 0 
2 4 7 
, 2
, 
5 0 0 
0 1 0 
6 3 5 
, 1
, 
3 0 0 
0 0 3 
4 5 2 
, 0
, 
6 0 0 
6 3 5 
1 2 4 
, 1
, 
0 0 3 
4 5 2 
3 3 3 
, 0
, 
5 6 3 
1 7 2 
5 0 0 
, 2
)
acting on the columns of the generator matrix as follows (in order):
(4, 9, 10)(6, 7, 8), 
(3, 7, 9)(4, 6, 8), 
(3, 6, 10)(4, 9, 8), 
(2, 8, 4, 9, 6, 7, 3), 
(2, 9, 10)(3, 8, 6), 
(1, 7, 2, 8, 6, 4, 3), 
(1, 3, 6, 2, 9, 10)(7, 8)
orbits: { 1, 3, 10, 9, 7, 6, 4, 2, 8 }, { 5 }