The generator matrix 1 0 0 1 1 1 X^2+X 1 X 1 X 1 1 X^2 1 X^2+X X^2+X 1 1 X^2+X 1 0 X^2 0 1 1 1 1 1 1 1 X^2+X X^2+X X 1 1 X 1 1 1 0 1 X 1 1 X^2+X 1 X^2 1 1 X 1 X^2 X^2+X 1 X^2 0 1 0 0 1 1 1 X^2 X^2 1 1 1 X^2+X X X^2+X 0 1 1 X 0 1 X^2 X^2+X X 1 1 1 1 X^2+X 1 X^2 1 X X^2 0 1 0 0 1 X+1 1 X^2 X^2 0 1 X^2+X+1 1 1 0 1 1 0 1 X^2 1 X^2+X 1 1 1 X^2+X X+1 X X^2+1 1 X X 1 1 X^2+X X^2+X+1 1 1 X^2+X X^2+X 1 X^2+1 0 X^2+1 X^2 1 X^2+1 1 X^2+X 0 X X X X^2 X+1 1 X X^2+1 0 1 X^2 X^2+1 X^2+1 1 1 X^2+X+1 1 X^2+X+1 X^2+X X^2+X X^2+X 1 X^2+1 X^2 X^2 1 0 X^2+X 1 1 X^2 X X+1 X^2+1 1 X^2+1 1 X^2+X 1 1 0 0 1 1 1 0 1 X^2+1 1 X^2 0 X^2+X+1 0 X^2+1 X+1 X^2+1 X^2 X^2 0 1 1 1 0 X^2+1 X^2+X X^2 X^2+X+1 X+1 X+1 X^2 X^2+1 1 X^2+X X^2+X+1 X^2+X X^2+X X^2+X+1 X^2+X+1 X^2+1 X^2+X 0 X 1 X X^2+1 X X+1 X^2 X^2+X+1 0 1 1 1 1 X^2+1 X^2+X+1 1 X^2+X 1 1 X^2+X+1 X+1 X^2+X+1 X^2+1 X^2+X 0 X^2 X^2+1 1 1 1 X^2 X 1 1 X^2+X X^2 1 0 X^2+X+1 X^2 X+1 X+1 X^2+1 X^2+X X X^2+X X^2+X+1 X^2+X+1 X^2+X+1 0 0 0 X 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2+X X X^2+X X X X^2+X X^2+X X X X X X^2+X X 0 0 0 0 X X^2 0 X X X^2 X X^2+X 0 X X X^2+X X^2 X^2 0 X 0 X^2+X X^2+X X^2+X X 0 X^2+X X 0 X^2 X^2 X X X^2+X X X^2 0 X^2+X X^2 0 X^2 0 X 0 0 X X^2 X^2 X^2 0 X^2 0 X 0 X^2+X X^2 X X^2 X^2+X X 0 X 0 0 0 0 X X^2 X X X^2+X X X X^2 X^2+X X^2 X^2 0 X^2 0 0 X^2 X^2+X X^2+X X X^2+X X^2+X X 0 X^2+X 0 0 X^2+X X^2 X X^2 X^2 X X^2 X^2+X X^2+X X^2 X X^2 X^2+X 0 0 0 X 0 X^2+X X^2+X 0 X^2 X^2 0 X^2+X X^2+X 0 X X^2 0 X^2+X X 0 X X X 0 X X^2+X X X^2 X^2+X 0 X^2 X X^2+X X^2 X^2+X X^2+X X^2 0 0 X^2 0 0 X^2+X X^2 X^2 X X^2 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+180x^82+208x^83+633x^84+376x^85+776x^86+540x^87+785x^88+492x^89+728x^90+492x^91+650x^92+396x^93+588x^94+288x^95+355x^96+148x^97+216x^98+92x^99+106x^100+28x^101+50x^102+12x^103+24x^104+16x^106+3x^108+6x^110+3x^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 6 seconds.