The reduced degree 8 case -- basis only:
10594:  0   1   2   0   3   1   4   5   2   3   6   4   7   5   6   7 
10684:  0   1   2   0   3   1   4   2   5   6   3   4   7   5   6   7 
10692:  0   1   2   0   3   1   4   2   5   3   6   7   4   5   6   7 
10694:  0   1   2   0   3   1   4   2   5   3   6   4   7   5   6   7 
10796:  0   1   2   0   3   1   2   3   4   5   6   4   7   5   6   7 
35025:  0   1   0   2   3   1   4   2   5   3   6   7   4   5   6   7 
35032:  0   1   0   2   3   1   4   2   5   3   6   4   7   5   6   7 
35059:  0   1   0   2   3   1   4   2   3   5   6   4   7   5   6   7 
38191:  0   1   0   2   1   3   4   2   5   3   6   7   4   5   6   7 
38198:  0   1   0   2   1   3   4   2   5   3   6   4   7   5   6   7 
38488:  0   1   0   2   1   3   2   4   5   3   6   4   7   5   6   7 
38518:  0   1   0   2   1   3   2   4   3   5   6   4   7   5   6   7 
38523:  0   1   0   2   1   3   2   4   3   5   4   6   5   7   6   7 
38551:  0   1   0   2   1   3   2   3   4   5   6   4   7   5   6   7 
38556:  0   1   0   2   1   3   2   3   4   5   4   6   5   7   6   7 
38810:  0   1   0   2   1   2   3   4   5   3   6   4   7   5   6   7 
38841:  0   1   0   2   1   2   3   4   3   5   6   4   7   5   6   7 
38846:  0   1   0   2   1   2   3   4   3   5   4   6   5   7   6   7 
41919:  0   1   0   1   2   3   4   2   5   3   6   7   4   5   6   7 
41926:  0   1   0   1   2   3   4   2   5   3   6   4   7   5   6   7 
42252:  0   1   0   1   2   3   2   4   5   3   6   4   7   5   6   7 
42287:  0   1   0   1   2   3   2   4   3   5   6   4   7   5   6   7 
42293:  0   1   0   1   2   3   2   4   3   5   4   6   5   7   6   7 
42298:  0   1   0   1   2   3   2   4   3   4   5   6   5   7   6   7 
42327:  0   1   0   1   2   3   2   3   4   5   6   4   7   5   6   7 
42333:  0   1   0   1   2   3   2   3   4   5   4   6   5   7   6   7 
42334:  0   1   0   1   2   3   2   3   4   5   4   5   6   7   6   7