length n = 60
dimension k = 3
alphabet length q = 5

minimum distance d = 48

generator matrix:
000000000011111111111111111111111111111111111111111111111111
010111111100010102020303040411121213131414222323242433343444
101011232300101020203030404011212131314141223232424233434344

projective group of automorphisms generated by:
100
001
010

100
001
010