The generator matrix 1 0 0 0 1 1 1 X 1 X 1 1 1 X X^2 1 0 X^2+X 1 1 X^2+X X^2 X^2 1 0 X 1 1 1 1 1 0 1 1 X^2 X^2+X 1 1 1 1 1 X^2+X X^2+X X 1 X^2+X X^2+X 1 X^2 X^2+X 1 X^2+X 1 X^2+X 0 1 1 1 1 X^2+X 1 1 1 0 X 1 X^2 0 1 1 1 0 1 1 1 1 X^2+X X 0 X 0 X^2 1 1 X^2+X X X^2 1 1 1 0 1 0 0 X 0 X X X^2+X+1 1 X^2+X+1 1 X^2+X+1 1 1 X^2+X 0 1 1 X^2+1 1 X^2+X 1 X 1 0 X^2+X X^2+1 X^2+1 X+1 X^2 1 X+1 X^2 X^2+X 1 X^2+1 0 1 0 X^2 1 0 1 X^2+X+1 X^2+X 1 X^2+X 1 X^2 0 1 X X 1 X^2+X+1 X^2 X^2+X X^2 X^2 1 0 X^2+1 X 1 X+1 X^2 0 X+1 X^2+X+1 X^2+X+1 1 X 0 X^2+1 0 1 X^2 1 1 1 0 X^2+X+1 1 1 1 X^2 X 0 X^2+X+1 0 0 1 0 X 1 X+1 1 X^2+X+1 X+1 X X^2+1 X^2 0 X+1 1 1 X^2+X X^2+1 X^2 1 X^2 1 X+1 X 1 0 X X+1 X^2+X X+1 X^2+X 0 1 1 0 X^2 X^2+X X^2+1 X+1 X X^2+1 0 X^2+1 1 X^2+X 1 0 X+1 1 0 X^2 X^2+1 1 0 X^2+X+1 1 X^2+X X^2 X 1 X^2 X^2 1 X^2+X+1 1 1 X X+1 0 0 1 X^2+1 X^2+X+1 X^2+X+1 X X 1 0 X^2+1 1 X^2 X^2 1 X^2+X X X^2+X 0 X^2+1 X^2+X 0 0 0 1 X+1 1 X X+1 X^2+1 X^2+X X^2+1 0 X X+1 1 X^2+X+1 X 1 X X X^2+1 1 X^2 0 X^2 0 X+1 1 X^2+1 X X X^2+1 0 X^2+X+1 X^2+X+1 X X^2+1 X^2+X+1 X^2+X+1 X^2+X+1 X^2 X 1 X^2 X^2+X 1 X^2+X+1 X^2+X X+1 1 X^2+X X^2+X+1 X+1 X^2+1 X^2+X 0 X+1 1 X^2+X 1 1 1 X^2+X+1 X^2+X X X^2+X+1 X^2 1 0 X+1 1 X^2+X+1 X^2 X X+1 X+1 1 1 X^2 0 X 1 X X^2+1 X+1 X^2 1 X^2 X^2+1 X^2+X 0 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 generates a code of length 90 over Z2[X]/(X^3) who´s minimum homogenous weight is 80. Homogenous weight enumerator: w(x)=1x^0+418x^80+252x^81+1232x^82+568x^83+2263x^84+892x^85+3032x^86+1184x^87+3746x^88+1264x^89+3502x^90+1284x^91+3678x^92+1084x^93+2956x^94+788x^95+1997x^96+544x^97+1136x^98+244x^99+360x^100+56x^101+148x^102+28x^103+58x^104+4x^105+18x^106+18x^108+8x^110+4x^112+1x^116 The gray image is a linear code over GF(2) with n=360, k=15 and d=160. This code was found by Heurico 1.16 in 76.7 seconds.