the 2 isometry classes of irreducible [10,7,3]_3 codes are:

code no       1:
================
1 1 1 2 0 0 0 0 0 0
1 1 0 0 2 0 0 0 0 0
2 1 0 0 0 2 0 0 0 0
1 0 1 0 0 0 2 0 0 0
2 0 1 0 0 0 0 2 0 0
0 1 1 0 0 0 0 0 2 0
2 1 1 0 0 0 0 0 0 2
the automorphism group has order 108
and is strongly generated by the following 7 elements:
(
2 0 0 
0 1 0 
0 0 1 
, 
2 0 0 
0 1 0 
1 0 1 
, 
1 0 0 
0 1 0 
2 0 1 
, 
2 0 0 
0 2 0 
1 1 1 
, 
2 0 0 
1 0 2 
2 2 0 
, 
2 0 0 
0 0 2 
0 2 0 
, 
2 0 0 
2 1 1 
2 2 0 
)
acting on the columns of the generator matrix as follows (in order):
(4, 10)(5, 6)(7, 8), 
(3, 7)(4, 9)(5, 6), 
(3, 7, 8)(4, 10, 9), 
(3, 4)(7, 9)(8, 10), 
(2, 8)(3, 5)(6, 7), 
(2, 3)(5, 7)(6, 8), 
(2, 8, 10)(3, 4, 5)(6, 7, 9)
orbits: { 1 }, { 2, 8, 3, 10, 7, 6, 4, 5, 9 }

code no       2:
================
1 1 1 2 0 0 0 0 0 0
1 1 0 0 2 0 0 0 0 0
2 1 0 0 0 2 0 0 0 0
1 0 1 0 0 0 2 0 0 0
2 0 1 0 0 0 0 2 0 0
0 1 1 0 0 0 0 0 2 0
0 2 1 0 0 0 0 0 0 2
the automorphism group has order 24
and is strongly generated by the following 4 elements:
(
1 0 0 
1 0 2 
1 2 0 
, 
2 0 0 
0 0 2 
0 2 0 
, 
0 1 2 
0 1 0 
2 1 0 
, 
2 1 0 
0 1 2 
0 1 0 
)
acting on the columns of the generator matrix as follows (in order):
(2, 8)(3, 6)(4, 9)(5, 7), 
(2, 3)(5, 7)(6, 8), 
(1, 10)(3, 6)(4, 7)(5, 9), 
(1, 8, 6)(2, 3, 10)(4, 5, 7)
orbits: { 1, 10, 6, 3, 8, 2 }, { 4, 9, 7, 5 }