The generator matrix 1 0 0 0 1 1 1 X^2 1 1 0 1 1 0 X 1 X^2+X 1 1 1 1 X^2+X X 1 0 1 1 X^2 X^2+X X^2+X 0 1 1 X^2+X 1 X^2 1 0 1 1 X X X^2+X 1 X 1 1 1 X 1 X 1 0 1 1 X^2 X^2 1 1 1 0 1 X^2+X X^2 X^2 1 X^2 1 X^2+X X X^2+X X^2 1 X 1 0 1 1 1 X^2+X 1 1 X^2+X 0 1 1 X 1 X^2 1 0 1 0 0 X X X^2+X 0 1 X^2+1 1 X^2+X+1 X+1 1 1 X^2+X 0 X+1 X+1 0 1 1 X X^2 X 1 X 1 1 1 1 X 1 0 X X^2 X^2+X 1 X^2+X+1 X+1 X^2+X 1 X^2 0 1 X^2 X X+1 1 X^2+1 1 X^2 1 0 X+1 1 X^2+X X X^2 1 1 1 X 1 1 X^2 X 1 X^2+X 1 1 0 X^2+X 1 X^2+1 X^2 X+1 X^2+X+1 1 X^2+X 0 0 1 X^2 X^2+X+1 X+1 1 X 1 0 0 0 1 0 X X^2+X+1 X^2+X+1 1 X+1 0 X X 1 X^2+1 X^2+1 X^2 1 X+1 X^2+X+1 X^2+1 X^2+X X+1 X^2+X X 1 X 1 X^2+X 1 X^2+X X+1 X^2+1 1 1 0 1 1 0 X^2+X X^2+X X^2 X 1 X^2+X X^2 X^2+X+1 0 X 1 X^2+X+1 X X^2+X X^2+X X+1 X+1 X^2+1 X^2 X+1 X^2+1 1 X^2 0 X X+1 X^2+1 X^2+X 0 1 1 0 X^2+X 0 X^2+X X^2+X+1 X^2 X X^2+X+1 X^2+1 X^2+1 1 X+1 0 X+1 0 X^2+1 X X^2+X+1 X X^2+1 0 0 0 0 1 X+1 X^2+X+1 X 1 X X+1 X+1 X^2+X 1 X^2+1 X 0 X^2+X+1 X^2 X^2+1 X+1 X^2+X X^2+X 1 X^2+X+1 X^2+X X^2+1 X^2+X X^2+1 X^2+1 X^2 0 X^2 X X X+1 X+1 X^2+1 X^2+1 X X+1 1 X^2+X+1 0 X^2+X X^2+X X^2 1 1 X X X^2+1 X+1 X+1 X X^2+X X 1 1 X X+1 X^2+X+1 0 1 X+1 X^2+X+1 X^2+1 1 X^2+X+1 X+1 X^2+1 X+1 1 0 X^2 1 1 X^2 1 0 X^2 X^2+X X^2+X+1 X+1 1 X^2+1 0 X^2+X X X+1 0 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 0 0 X^2 0 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 0 0 0 X^2 0 0 generates a code of length 90 over Z2[X]/(X^3) who´s minimum homogenous weight is 82. Homogenous weight enumerator: w(x)=1x^0+176x^82+210x^83+605x^84+482x^85+782x^86+502x^87+783x^88+522x^89+734x^90+366x^91+692x^92+366x^93+537x^94+282x^95+402x^96+170x^97+229x^98+84x^99+91x^100+52x^101+63x^102+24x^103+17x^104+4x^105+5x^106+4x^107+4x^109+2x^110+1x^112 The gray image is a linear code over GF(2) with n=360, k=13 and d=164. This code was found by Heurico 1.16 in 4.87 seconds.