the 3 isometry classes of irreducible [7,2,4]_3 codes are:

code no       1:
================
1 1 1 1 1 2 0
1 1 1 0 0 0 2
the automorphism group has order 72
and is strongly generated by the following 4 elements:
(
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
2 2 2 2 2 
, 
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
2 2 2 2 2 
0 0 0 1 0 
, 
1 0 0 0 0 
0 0 1 0 0 
0 1 0 0 0 
0 0 0 0 1 
2 2 2 2 2 
, 
2 2 2 2 2 
0 0 0 1 0 
0 0 0 0 1 
0 0 1 0 0 
1 0 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(5, 6), 
(4, 5, 6), 
(2, 3)(4, 6, 5), 
(1, 5, 3, 4, 2, 6)
orbits: { 1, 6, 5, 4, 2, 3 }, { 7 }

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

code no       3:
================
1 1 1 0 0 2 0
1 1 0 1 1 0 2
the automorphism group has order 48
and is strongly generated by the following 5 elements:
(
2 0 0 0 0 
0 2 0 0 0 
0 0 2 0 0 
0 0 0 2 0 
1 1 0 1 1 
, 
2 0 0 0 0 
0 2 0 0 0 
0 0 2 0 0 
0 0 0 0 2 
0 0 0 2 0 
, 
2 0 0 0 0 
0 2 0 0 0 
0 0 2 0 0 
1 1 0 1 1 
0 0 0 2 0 
, 
1 0 0 0 0 
0 1 0 0 0 
2 2 2 0 0 
0 0 0 1 0 
0 0 0 0 1 
, 
2 2 2 0 0 
0 0 1 0 0 
0 1 0 0 0 
0 0 0 2 0 
0 0 0 0 2 
)
acting on the columns of the generator matrix as follows (in order):
(5, 7), 
(4, 5), 
(4, 5, 7), 
(3, 6), 
(1, 6)(2, 3)
orbits: { 1, 6, 3, 2 }, { 4, 5, 7 }