length n = 243
dimension k = 7
alphabet length q = 3

minimum distance d = 154

generator matrix:
000001000001000000000011111000000000000000000001111111111000001111111111000001111111111000000000000000000001111111111111111111111111111111111111111011111000001111111111111111111111111000000000011111111111111111111111111111111111111111111111111
000010000010000000111100001000000000000111111110000000022011110000111111011110000111111000011111111111111110000000000000000111111111111222222222222101111111110000011111111111122222222111111111100000000001111111111111111222222222222222222222222
000100000100000111000100010000000111111000000220000002200101110111000111101110111000111111100001111112222220000111111222222000000111222000000111222110111111221112200011111122200111222111122222211112222220000111222222222000000111111111222222222
001000001000011001001000100001111000022000022000000220000110111011011001110111011011001112211220011220011221122001122001122001122002001001122001002111011112121121211200112201112011022122211122212221112221222022000112222111222000112222000111122
010000010000101010010001000110022002200002200000022000000111011101101010111011101101010121212121202011201021212120201120102120201020010120102010020111101121121211212112020110112101202212212211221221221122122202122020012122112122020012112001201
100000100000110100100010000222200220000220000002200000000111101110110100111101110110100211221122120101210202112212010121020212010200100121020100200111110211122111221121201011012110220221221212122122121212212220212201200212121212201200121120010
000000222222222222222222222121212121212121212121212121212000000000000000222222222222222111211121111111211221112111111121122111111111111121122111222222222222212222122222222222221222111111211212211121121221112111112111212112122112111212122121222

projective group of automorphisms generated by:
0001000
0000010
0100000
0000100
0010000
1000000
0000001

1000000
0001000
0010000
0000010
0100000
0000100
0000001