the 7 isometry classes of irreducible [11,4,6]_3 codes are:

code no       1:
================
1 1 1 1 1 1 1 2 0 0 0
2 2 1 1 1 0 0 0 2 0 0
2 1 2 1 0 1 0 0 0 2 0
0 2 2 2 1 1 0 0 0 0 2
the automorphism group has order 16
and is strongly generated by the following 4 elements:
(
2 0 0 0 0 0 0 
0 2 0 0 0 0 0 
0 0 2 0 0 0 0 
0 0 0 2 0 0 0 
0 0 0 0 2 0 0 
0 0 0 0 0 2 0 
1 1 1 1 1 1 1 
, 
2 0 0 0 0 0 0 
0 0 2 0 0 0 0 
0 2 0 0 0 0 0 
0 0 0 2 0 0 0 
0 0 0 0 0 2 0 
0 0 0 0 2 0 0 
0 0 0 0 0 0 2 
, 
0 1 1 1 2 2 0 
2 2 1 1 1 0 0 
2 1 2 1 0 1 0 
0 0 0 1 0 0 0 
0 0 0 0 0 1 0 
0 0 0 0 1 0 0 
0 0 0 0 0 0 1 
, 
0 0 0 0 0 1 0 
0 2 0 0 0 0 0 
1 2 1 2 0 2 0 
0 0 0 2 0 0 0 
0 1 1 1 2 2 0 
1 0 0 0 0 0 0 
1 1 1 1 1 1 1 
)
acting on the columns of the generator matrix as follows (in order):
(7, 8), 
(2, 3)(5, 6)(9, 10), 
(1, 11)(2, 9)(3, 10)(5, 6), 
(1, 6)(3, 10)(5, 11)(7, 8)
orbits: { 1, 11, 6, 5 }, { 2, 3, 9, 10 }, { 4 }, { 7, 8 }

code no       2:
================
1 1 1 1 1 1 1 2 0 0 0
2 2 1 1 1 0 0 0 2 0 0
2 1 2 1 0 1 0 0 0 2 0
1 2 2 1 0 0 1 0 0 0 2
the automorphism group has order 12
and is strongly generated by the following 2 elements:
(
2 0 0 0 0 0 0 
0 0 2 0 0 0 0 
0 2 0 0 0 0 0 
0 0 0 2 0 0 0 
0 0 0 0 0 2 0 
0 0 0 0 2 0 0 
0 0 0 0 0 0 2 
, 
2 1 2 1 0 1 0 
1 2 2 1 0 0 1 
2 2 1 1 1 0 0 
1 1 1 1 1 1 1 
0 0 0 0 1 0 0 
0 0 0 0 0 0 1 
0 0 0 0 0 1 0 
)
acting on the columns of the generator matrix as follows (in order):
(2, 3)(5, 6)(9, 10), 
(1, 10)(2, 11)(3, 9)(4, 8)(6, 7)
orbits: { 1, 10, 9, 3, 2, 11 }, { 4, 8 }, { 5, 6, 7 }

code no       3:
================
1 1 1 1 1 1 1 2 0 0 0
2 2 1 1 1 0 0 0 2 0 0
2 1 2 1 0 1 0 0 0 2 0
2 1 0 1 2 0 1 0 0 0 2
the automorphism group has order 16
and is strongly generated by the following 3 elements:
(
2 0 0 0 0 0 0 
0 2 0 0 0 0 0 
0 0 0 0 2 0 0 
0 0 0 2 0 0 0 
0 0 2 0 0 0 0 
0 0 0 0 0 0 2 
0 0 0 0 0 2 0 
, 
2 0 0 0 0 0 0 
0 0 0 0 1 0 0 
2 2 1 1 1 0 0 
0 0 0 2 0 0 0 
0 1 0 0 0 0 0 
1 2 1 2 0 2 0 
0 0 0 0 0 0 2 
, 
2 0 0 0 0 0 0 
1 2 1 2 0 2 0 
2 1 0 1 2 0 1 
1 1 1 1 1 1 1 
0 0 0 0 0 0 1 
0 2 0 0 0 0 0 
0 0 1 0 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(3, 5)(6, 7)(10, 11), 
(2, 5)(3, 9)(6, 10), 
(2, 6, 9, 10)(3, 7, 5, 11)(4, 8)
orbits: { 1 }, { 2, 5, 10, 3, 7, 11, 6, 9 }, { 4, 8 }

code no       4:
================
1 1 1 1 1 1 1 2 0 0 0
2 2 1 1 1 0 0 0 2 0 0
2 1 2 1 0 1 0 0 0 2 0
0 2 2 1 2 0 1 0 0 0 2
the automorphism group has order 6
and is strongly generated by the following 2 elements:
(
1 0 0 0 0 0 0 
0 2 2 1 2 0 1 
0 0 0 2 0 0 0 
0 0 0 0 0 0 1 
0 1 0 0 0 0 0 
1 1 1 1 1 1 1 
0 0 2 0 0 0 0 
, 
1 1 2 2 2 0 0 
0 0 1 0 0 0 0 
0 1 0 0 0 0 0 
0 0 0 0 2 0 0 
0 0 0 2 0 0 0 
1 2 1 2 0 2 0 
0 1 1 2 1 0 2 
)
acting on the columns of the generator matrix as follows (in order):
(2, 5, 11)(3, 7, 4)(6, 10, 8), 
(1, 9)(2, 3)(4, 5)(6, 10)(7, 11)
orbits: { 1, 9 }, { 2, 11, 3, 5, 7, 4 }, { 6, 8, 10 }

code no       5:
================
1 1 1 1 1 0 0 2 0 0 0
2 2 1 1 0 1 0 0 2 0 0
2 1 2 0 1 1 0 0 0 2 0
2 1 2 1 0 0 1 0 0 0 2
the automorphism group has order 144
and is strongly generated by the following 4 elements:
(
1 0 0 0 0 0 0 
0 1 0 0 0 0 0 
0 0 1 0 0 0 0 
0 0 0 1 0 0 0 
0 0 0 0 1 0 0 
0 0 0 0 0 1 0 
1 2 1 2 0 0 2 
, 
2 0 0 0 0 0 0 
0 2 0 0 0 0 0 
0 0 0 1 0 0 0 
0 0 1 0 0 0 0 
1 1 2 2 0 2 0 
2 2 2 2 2 0 0 
0 0 0 0 0 0 2 
, 
1 0 0 0 0 0 0 
2 2 2 2 2 0 0 
0 0 1 0 0 0 0 
0 0 0 0 1 0 0 
0 0 0 1 0 0 0 
2 1 2 0 1 1 0 
0 0 0 0 0 0 2 
, 
2 1 2 0 1 1 0 
0 0 1 0 0 0 0 
1 1 2 2 0 2 0 
1 1 1 1 1 0 0 
0 0 0 0 1 0 0 
0 2 0 0 0 0 0 
0 0 0 0 0 0 2 
)
acting on the columns of the generator matrix as follows (in order):
(7, 11), 
(3, 4)(5, 9)(6, 8), 
(2, 8)(4, 5)(6, 10), 
(1, 8, 4, 10)(2, 6, 9, 3)
orbits: { 1, 10, 6, 4, 8, 2, 3, 5, 9 }, { 7, 11 }

code no       6:
================
1 1 1 1 1 0 0 2 0 0 0
2 2 1 1 0 1 0 0 2 0 0
2 1 2 0 1 1 0 0 0 2 0
1 2 0 2 1 1 1 0 0 0 2
the automorphism group has order 288
and is strongly generated by the following 4 elements:
(
1 0 0 0 0 0 0 
0 1 0 0 0 0 0 
0 0 1 0 0 0 0 
0 0 0 1 0 0 0 
0 0 0 0 1 0 0 
0 0 0 0 0 1 0 
2 1 0 1 2 2 2 
, 
2 0 0 0 0 0 0 
0 2 0 0 0 0 0 
0 0 0 1 0 0 0 
0 0 1 0 0 0 0 
1 1 2 2 0 2 0 
2 2 2 2 2 0 0 
0 0 0 0 0 0 2 
, 
1 0 0 0 0 0 0 
0 0 0 2 0 0 0 
1 2 1 0 2 2 0 
1 1 1 1 1 0 0 
0 0 0 0 0 1 0 
2 2 1 1 0 1 0 
0 0 0 0 0 0 2 
, 
1 2 1 0 2 2 0 
0 0 0 1 0 0 0 
0 0 0 0 0 1 0 
0 0 0 0 2 0 0 
2 2 2 2 2 0 0 
2 0 0 0 0 0 0 
0 0 0 0 0 0 2 
)
acting on the columns of the generator matrix as follows (in order):
(7, 11), 
(3, 4)(5, 9)(6, 8), 
(2, 9, 6, 5, 10, 3, 8, 4), 
(1, 6, 3, 10)(2, 8, 5, 4)
orbits: { 1, 10, 5, 3, 9, 6, 8, 4, 2 }, { 7, 11 }

code no       7:
================
1 1 1 1 1 0 0 2 0 0 0
2 2 1 1 0 1 0 0 2 0 0
2 1 2 1 0 0 1 0 0 2 0
1 2 2 0 1 1 1 0 0 0 2
the automorphism group has order 48
and is strongly generated by the following 4 elements:
(
2 0 0 0 0 0 0 
0 2 0 0 0 0 0 
0 0 2 0 0 0 0 
0 0 0 2 0 0 0 
1 1 1 1 1 0 0 
2 2 1 1 0 1 0 
2 1 2 1 0 0 1 
, 
1 0 0 0 0 0 0 
0 1 0 0 0 0 0 
0 0 0 2 0 0 0 
0 0 2 0 0 0 0 
2 2 1 1 0 1 0 
1 1 1 1 1 0 0 
0 0 0 0 0 0 1 
, 
1 0 0 0 0 0 0 
0 0 1 0 0 0 0 
0 0 0 2 0 0 0 
0 2 0 0 0 0 0 
2 1 2 1 0 0 1 
1 1 1 1 1 0 0 
0 0 0 0 0 1 0 
, 
0 0 2 0 0 0 0 
0 0 0 2 0 0 0 
0 1 0 0 0 0 0 
1 0 0 0 0 0 0 
2 2 1 1 0 1 0 
0 0 0 0 1 0 0 
2 1 2 1 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(5, 8)(6, 9)(7, 10), 
(3, 4)(5, 9)(6, 8), 
(2, 4, 3)(5, 9, 10)(6, 7, 8), 
(1, 4, 2, 3)(5, 6, 8, 9)(7, 10)
orbits: { 1, 3, 4, 2 }, { 5, 8, 9, 10, 6, 7 }, { 11 }