The generator matrix 1 0 1 1 1 X^2 1 1 0 1 1 0 1 1 X^2 1 1 X^2 1 X^2 1 X 1 1 1 1 X^2+X 1 1 X^2+X 1 X 1 1 1 X^2+X 1 X^2 1 X^2 1 X^2+X 1 1 X^2 X^2 1 X 1 1 X^2+X 1 X^2+X 1 1 X^2+X 0 X^2+X 0 X 1 1 1 0 X^2+X 1 1 X^2+X 1 X 1 1 1 X^2 1 1 1 1 X^2 0 1 1 1 X^2 1 1 1 0 1 1 0 1 1 X^2 X+1 1 1 0 1 X+1 0 1 X+1 0 1 X+1 1 0 1 0 X^2+1 X^2 X^2+X+1 1 X+1 X^2+X 1 X+1 1 X X X^2+X+1 1 X 1 0 1 X^2 1 1 X^2+1 1 1 X^2+X 1 X^2+X+1 X^2 1 X^2+X 1 1 X 1 1 1 1 1 X^2 X^2+X+1 X^2+1 1 1 1 X^2+X 1 X^2+X 0 0 X 1 1 1 X X^2+1 1 1 1 X^2+X X^2+1 X^2+X+1 1 X^2 X^2+X 1 0 0 X 0 0 0 0 0 0 0 0 0 0 X^2+X X^2+X X X X^2+X X^2+X X X^2+X X^2+X X^2+X X X^2 X^2 X^2+X X^2 X X^2 X^2 X^2 X X^2+X X^2+X X X X^2+X X^2 X^2 X 0 X^2 0 X X^2 X^2 X^2 X^2+X X^2+X X^2 0 X^2 X 0 X X 0 X^2 X^2+X X^2 X^2 X^2+X X X^2+X X^2+X X^2 X^2 X^2 0 X^2+X X X^2 0 X^2 X X X^2 X^2+X X^2+X X^2 X^2 X^2+X X^2 X^2+X X^2+X X^2+X 0 0 0 X 0 0 X^2 X^2 X^2+X X^2+X X X X^2+X X^2 X X^2 X^2+X X X X^2 X^2+X X^2 0 X^2+X X X X 0 X^2 X^2 X^2+X 0 X X X^2 0 X^2 X^2+X X^2 X 0 X^2 X^2+X X^2 0 X^2 X X X^2 X X^2+X X X^2+X X X^2 X X^2+X X X 0 0 X^2 X^2+X 0 X^2 0 0 0 X^2+X 0 X^2 0 X X^2 X^2 X^2+X X^2 X X^2 X^2+X 0 X^2+X X X^2+X 0 0 X^2+X 0 0 0 0 X X^2+X X^2+X 0 X X^2 X X^2 X^2+X X^2+X X^2+X X^2+X X^2 0 X^2 X X X^2 0 X^2+X X^2 0 X^2 X^2+X X X^2+X X^2+X X^2 X 0 0 X^2 X^2 X^2+X X X^2 X X^2+X 0 X^2 X^2+X X^2 X^2 X^2+X X 0 X X^2+X X^2+X X X^2 X^2+X X 0 X^2+X X 0 X^2+X 0 X^2 X X X^2+X X^2+X X^2+X X^2+X X^2 X^2+X X X X^2+X X X^2+X X^2 X X^2 X X^2 X^2+X X^2+X X^2+X X^2+X X^2+X generates a code of length 87 over Z2[X]/(X^3) who´s minimum homogenous weight is 80. Homogenous weight enumerator: w(x)=1x^0+230x^80+104x^81+440x^82+160x^83+485x^84+188x^85+472x^86+124x^87+474x^88+192x^89+406x^90+152x^91+251x^92+92x^93+182x^94+12x^95+57x^96+14x^98+26x^100+18x^102+5x^104+4x^106+5x^108+1x^116+1x^120 The gray image is a linear code over GF(2) with n=348, k=12 and d=160. This code was found by Heurico 1.16 in 2.09 seconds.