length n = 44
dimension k = 4
alphabet length q = 7

minimum distance d = 36

generator matrix:
00011111111100011111111100111111111111111111
11100011224411100011666611002244112234456666
12412402010416616606001624240402462561621346
21421420104061661660160042424020645266124613

projective group of automorphisms generated by:
1000
0010
0001
0100

0100
0010
0001
1000