length n = 27
dimension k = 6
alphabet length q = 4

minimum distance d = 16

generator matrix:

0	0	0	0	0	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
0	0	1	1	1	0	0	0	1	1	1	1	1	1	1	2	3	1	2	2	3	3	1	2	2	3	3
1	1	0	0	1	0	0	1	0	1	1	1	1	1	3	2	1	2	1	3	2	3	3	2	3	1	2
0	1	0	1	1	1	1	0	0	0	1	1	1	3	1	2	1	3	3	2	2	1	2	1	3	2	3
1	0	1	1	0	0	1	1	0	0	1	1	3	1	1	2	1	3	2	3	1	2	2	3	1	3	2
1	1	1	0	0	1	0	0	1	0	1	3	1	1	1	2	1	2	3	1	3	2	3	3	2	2	1

projective group of automorphisms generated by:

0	2	0	0	0	0
0	0	0	0	0	2
2	0	0	0	0	0
0	0	0	2	0	0
0	0	2	0	0	0
0	0	0	0	2	0

0	0	0	0	0	2
2	0	0	0	0	0
0	0	0	2	0	0
0	0	0	0	2	0
0	0	2	0	0	0
0	2	0	0	0	0