the 1 isometry classes of irreducible [20,8,8]_2 codes are:

code no       1:
================
1 1 1 1 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0
1 1 1 1 0 0 0 1 1 1 0 0 0 1 0 0 0 0 0 0
1 1 0 0 1 1 0 1 1 0 1 0 0 0 1 0 0 0 0 0
1 0 1 0 1 0 1 1 0 1 1 0 0 0 0 1 0 0 0 0
1 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 1 0 0 0
0 1 1 0 1 0 1 1 1 0 0 1 0 0 0 0 0 1 0 0
1 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 1 0
0 1 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 1
the automorphism group has order 23040
and is strongly generated by the following 8 elements:
(
1 0 0 0 0 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 
0 0 0 0 0 0 1 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 
1 1 1 1 0 0 0 1 1 1 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 
1 0 1 0 1 0 1 1 0 1 1 0 
1 1 0 0 0 1 1 1 0 1 0 1 
, 
1 0 0 0 0 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 
0 0 0 0 0 0 1 0 0 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 
1 1 1 1 0 0 0 1 1 1 0 0 
1 1 0 0 1 1 0 1 1 0 1 0 
0 1 1 0 1 0 1 1 1 0 0 1 
, 
1 0 0 0 0 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 
1 1 1 1 1 1 1 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 
1 1 0 0 0 1 1 1 0 1 0 1 
0 0 0 0 0 0 0 0 0 0 0 1 
0 1 1 0 1 0 1 1 1 0 0 1 
0 0 0 0 0 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 
, 
1 0 0 0 0 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 
1 1 0 0 1 1 0 1 1 0 1 0 
1 0 1 0 1 0 1 1 0 1 1 0 
0 0 0 0 1 0 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 
0 0 0 0 0 0 1 0 0 0 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 
1 1 0 0 0 1 1 1 0 1 0 1 
, 
1 0 0 0 0 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 
1 1 1 1 0 0 0 1 1 1 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 
1 0 1 0 1 0 1 1 0 1 1 0 
1 0 0 1 0 1 1 0 1 1 1 0 
0 0 0 0 0 0 0 0 0 0 1 0 
0 0 0 0 0 1 0 0 0 0 0 0 
0 1 1 0 1 0 1 1 1 0 0 1 
, 
1 0 0 0 0 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 
0 0 0 0 0 0 1 0 0 0 0 0 
1 0 1 0 1 0 1 1 0 1 1 0 
1 0 0 1 0 1 1 0 1 1 1 0 
1 1 0 0 1 1 0 1 1 0 1 0 
1 1 1 1 0 0 0 1 1 1 0 0 
0 1 1 0 1 0 1 1 1 0 0 1 
, 
1 0 0 0 0 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 
0 0 0 0 0 0 1 0 0 0 0 0 
1 1 1 1 1 1 1 0 0 0 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 
1 1 1 1 0 0 0 1 1 1 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 
1 1 0 0 0 1 1 1 0 1 0 1 
, 
0 0 0 0 1 0 0 0 0 0 0 0 
0 0 0 0 0 0 1 0 0 0 0 0 
1 1 1 1 1 1 1 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 
1 0 0 1 0 1 1 0 1 1 1 0 
1 1 0 0 1 1 0 1 1 0 1 0 
0 0 0 0 0 0 0 0 0 0 1 0 
0 0 0 0 0 0 0 0 0 1 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 
0 1 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(8, 10)(9, 14)(11, 16)(12, 19)(15, 17)(18, 20), 
(8, 9)(10, 14)(11, 15)(12, 18)(16, 17)(19, 20), 
(6, 7, 13)(8, 17, 19)(9, 11, 12)(10, 16, 18)(14, 15, 20), 
(5, 8, 11)(6, 9, 15)(7, 10, 16)(12, 18, 19)(13, 14, 17), 
(5, 15, 14)(6, 11, 10)(7, 17, 9)(8, 13, 16)(12, 19, 18), 
(3, 4)(5, 6)(8, 16)(9, 17)(10, 15)(11, 14)(12, 18), 
(2, 4, 3)(6, 13, 7)(9, 14, 10)(12, 18, 19)(15, 17, 16), 
(1, 17, 5)(2, 11, 7)(3, 16, 13)(4, 15, 6)(8, 9, 10)
orbits: { 1, 5, 11, 14, 6, 17, 16, 15, 9, 8, 2, 10, 20, 13, 7, 3, 4, 12, 19, 18 }