The generator matrix 1 0 1 1 1 0 1 X^2+X 1 X^2 1 1 X 1 1 1 X^2+X 1 1 X^2 X^2+X 1 1 1 X^2+X 1 1 1 X^2+X 1 X^2 1 1 1 1 1 1 X 1 X 1 X 1 X^2+X 1 1 1 1 X 1 1 1 X^2 X X^2 X^2 1 0 1 1 1 X^2 1 0 1 1 1 X 1 1 1 0 1 X 1 1 1 1 X^2 X^2 0 0 1 1 1 1 0 1 1 0 X^2+X+1 1 X 1 X+1 1 X^2+1 X^2+X 1 0 1 X 1 X+1 X^2 1 1 X^2+X+1 X^2+X+1 X^2+X 1 1 X 1 1 0 1 X^2+1 X^2 1 X X+1 X^2+X+1 1 X^2+X+1 1 1 1 X^2+X 1 X^2+X+1 0 X^2+X 1 1 0 1 X^2+1 1 1 1 1 X^2+1 1 X+1 X+1 X+1 1 X^2+X+1 0 X^2+X+1 X^2+X+1 1 X^2+X X^2+1 X^2+X+1 X 1 X^2+X 0 1 X^2 X^2+X X+1 1 1 1 1 X^2+X+1 X^2 X^2 X^2 0 0 X 0 X^2+X X 0 X X^2+X X X 0 X^2+X X X^2 X X^2 X^2 X^2+X 0 0 X X^2 X 0 X^2 X^2+X 0 0 X^2+X X^2+X X^2+X X X^2 X^2+X X^2 X 0 X^2+X X^2 X^2 X^2+X 0 X 0 0 X^2 X^2+X X X^2 X^2+X X^2 X^2 X^2+X 0 0 X X^2 X^2+X 0 0 X^2+X X^2+X X 0 X^2 0 X^2+X 0 X X^2 X^2 0 X^2+X X^2 X 0 X^2 X X 0 X^2+X X X 0 X^2+X 0 0 0 X 0 X X X X X^2 X^2+X X^2 0 X X X^2 0 0 X^2 X^2+X X^2+X 0 X X 0 X^2 X^2 X 0 X^2+X X X X^2 0 X X^2 X X 0 X X^2+X X X^2 0 0 X^2+X X X^2+X X^2 0 0 X^2 X^2+X X X 0 X^2 X^2 X X^2+X X X^2+X X^2 X^2 X 0 0 X^2+X X^2 0 X^2 0 X 0 X^2+X X^2+X 0 X^2+X X^2+X X^2 X^2 X X^2+X 0 X X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 X^2 0 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 generates a code of length 86 over Z2[X]/(X^3) who´s minimum homogenous weight is 80. Homogenous weight enumerator: w(x)=1x^0+137x^80+132x^81+252x^82+156x^83+217x^84+124x^85+188x^86+104x^87+181x^88+112x^89+124x^90+92x^91+92x^92+44x^93+40x^94+17x^96+4x^97+16x^98+7x^100+4x^102+2x^104+1x^112+1x^120 The gray image is a linear code over GF(2) with n=344, k=11 and d=160. This code was found by Heurico 1.16 in 0.734 seconds.