The generator matrix 1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 X 1 1 1 0 1 1 1 1 1 0 1 1 1 0 1 X 1 X 1 2X 2X 1 1 1 1 1 1 1 1 2X X 1 1 1 0 X 0 1 1 1 X 1 0 1 1 2 0 1 2 1 0 2X+1 2 1 0 2 2X+1 1 2X+1 1 2 0 2 1 2X+1 0 2 2X+1 X 1 X+2 2X+1 0 1 2X 1 2X+1 1 0 1 1 2X X+2 2X+2 X+2 2X+1 X 2X+1 2X 1 1 1 2X+2 1 1 1 1 X X+1 2 0 2X+1 0 0 2X 0 0 0 0 0 0 2X X 2X 2X 2X 2X 0 X 2X X 0 2X 0 2X X 2X 0 0 X X 0 0 X 2X X X 2X 0 0 2X 2X 2X 2X 0 X X X 0 0 X 0 2X X X 0 0 0 X 2X X 2X 0 0 0 X 0 0 0 0 0 0 0 0 0 0 2X X X 2X 2X X X X 2X 0 X X 0 X 0 X X X 2X X 0 2X 2X 2X X 0 0 0 2X 2X 2X 0 2X 0 0 2X X 2X 2X 0 2X 0 0 0 X X 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X 2X 2X 2X 2X X 2X 2X X 2X X 2X X X 2X 2X X 0 X X 2X X X 0 X 0 X 2X 0 2X X 0 2X 0 X 2X X 0 X 2X 0 0 0 0 0 0 2X 0 0 X 2X 2X X 2X 0 2X 2X X 2X 2X X 0 0 0 2X X 0 2X 0 X 0 2X 2X 2X 2X 2X 0 2X X X X X 0 X X X 2X 2X 0 0 2X X X X 0 0 0 0 2X 0 0 0 0 0 0 0 0 X 0 X 0 X X X 2X 2X X X 0 0 X 0 2X 2X X 2X X 0 0 0 X 0 0 X X 2X 0 0 0 X X 0 2X 0 0 2X 2X 2X X 2X X X 0 0 0 0 2X X 2X 2X 0 0 0 0 0 0 0 0 X X X X 0 2X X 2X 0 2X 2X 0 0 X 2X 2X 2X 0 X 2X 2X X 2X 2X 0 0 2X X X 2X 0 X 0 0 X 0 2X 0 X X 0 X 0 0 X X 2X 2X 2X X 0 X X generates a code of length 60 over Z3[X]/(X^2) who´s minimum homogenous weight is 99. Homogenous weight enumerator: w(x)=1x^0+144x^99+6x^100+6x^101+310x^102+24x^103+24x^104+674x^105+222x^106+216x^107+1158x^108+444x^109+528x^110+2138x^111+930x^112+1224x^113+3608x^114+1734x^115+2064x^116+5136x^117+2664x^118+2742x^119+5792x^120+2640x^121+2970x^122+5660x^123+2274x^124+1902x^125+4056x^126+1398x^127+1098x^128+2254x^129+618x^130+318x^131+998x^132+144x^133+30x^134+456x^135+24x^136+218x^138+122x^141+34x^144+32x^147+8x^150+4x^153+2x^156 The gray image is a linear code over GF(3) with n=180, k=10 and d=99. This code was found by Heurico 1.16 in 58.6 seconds.