The generator matrix 1 0 0 0 1 1 1 0 1 1 1 1 X^2 X^2+X X X 1 X X^2+X 1 1 X^2 0 X 1 1 1 1 X^2+X 1 0 1 X^2+X 1 X^2+X 1 1 1 1 1 X^2+X 1 1 X^2+X 1 1 X 1 X X^2 1 X 1 1 X^2+X X X^2+X 1 1 X 1 1 0 0 X^2+X X X X^2+X 1 1 1 X^2 0 X^2 1 X X X^2 X^2+X 1 1 X^2 X^2 X^2 0 1 0 0 X^2+X 1 0 1 0 0 1 X^2 1 1 X^2+1 0 X^2+X+1 X 1 X^2+X 1 1 X^2+1 0 1 X^2+X 0 1 1 X^2+X X^2 X^2+X+1 X+1 X^2+X 0 1 1 X^2+1 X^2 X^2 X^2 X^2+X+1 X X X 1 1 X^2+X X^2+X 1 X^2+1 X^2+X+1 X X^2+X+1 1 0 X^2 X^2+X X^2 X^2+1 X 1 1 X X^2+X+1 1 0 X 1 X^2 X^2 X^2 1 1 1 X^2 X 1 1 1 1 1 X^2 1 X X^2 1 X^2+X X^2+X 1 1 X^2 1 1 0 0 0 0 1 0 X 0 X^2+X X 1 1 X+1 X^2+X+1 X+1 1 X^2+1 X^2+X X^2+X 1 X^2+X+1 X X^2+X+1 X^2+1 0 X X X^2+1 X^2+X 1 1 X+1 1 X^2+X 1 0 X^2 X^2+X X^2 X^2+X+1 X+1 X^2+1 0 1 0 X^2 1 X^2 0 X^2+1 X^2+1 1 X^2+1 X^2+X X^2+1 X^2 1 X^2+X+1 X^2 X^2 0 1 X^2+X+1 1 X^2 1 1 X X^2 X^2+1 X^2 X^2+X+1 X^2+1 X^2+X X^2+X X+1 X+1 X^2+X 1 X+1 1 X 0 X 1 X^2+X X^2+X+1 X+1 1 X 1 0 0 0 0 1 X 1 X+1 X+1 X+1 X 0 1 X^2+1 X^2+X+1 X^2+X X X^2 0 X^2+X+1 X^2 X^2+1 X^2 X+1 1 X^2+X+1 X^2 X+1 0 X^2+X+1 X^2+X+1 X^2+X 1 X X^2+X+1 1 X^2 X^2 X^2+X 1 0 1 X^2+X X^2+1 X^2 X^2+1 X^2+1 1 X X 0 X^2 1 X^2+X X^2+X+1 X X X+1 X X+1 1 X^2 X+1 X^2+X+1 X+1 1 1 X+1 X^2+1 X^2+X X^2+X X^2+X X+1 0 X X X^2+1 X^2 1 0 1 X^2+X+1 1 X^2+X+1 X+1 X^2+1 X^2+X+1 0 X X^2+1 X 0 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 0 0 0 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 X^2 X^2 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+95x^82+348x^83+425x^84+672x^85+581x^86+748x^87+556x^88+766x^89+480x^90+582x^91+521x^92+554x^93+371x^94+432x^95+282x^96+252x^97+149x^98+148x^99+58x^100+62x^101+46x^102+28x^103+10x^104+10x^105+6x^106+2x^107+2x^108+4x^109+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 1.11 in 1.72 seconds.