The generator matrix 1 0 0 0 1 1 1 0 1 1 1 1 X^2 0 X X 1 X^2 X^2 1 X 1 1 X 1 1 1 1 X X 1 1 1 0 X 1 1 X^2 X^2+X X^2+X X 1 1 0 1 1 1 1 X^2 0 X 1 1 X 0 1 X^2+X X^2+X 1 X 0 1 X^2+X 1 X 0 1 X X 1 0 X^2 1 1 X^2+X 1 X 1 1 1 0 X^2 1 1 1 X^2+X X^2 1 0 1 0 0 1 X^2 1 1 X^2+1 0 X^2+X+1 X 1 X 1 1 X+1 X 1 X^2+X 1 X^2+X+1 X+1 X X^2 X^2 X^2+X+1 0 1 0 X^2+X+1 X+1 X^2+X+1 1 1 X^2 X^2+X+1 1 X^2+X X^2 0 0 X^2 X X X^2 X X^2+X+1 X^2+X 1 1 X^2 X+1 0 1 1 1 1 X 0 1 X^2+X 1 X^2+1 X X X^2+1 1 1 0 1 1 X 1 X X^2+X X^2 X+1 X^2+X X^2+X+1 1 1 X X X 1 1 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 1 0 X^2 X+1 X^2+X+1 X X^2+X 1 X+1 1 X^2 1 1 X^2+X+1 X^2+X 0 X^2+X X^2+X X X^2+X X+1 1 1 0 1 X^2+1 1 X^2+X X^2+X X+1 1 X^2+X X^2 X+1 X^2+X 1 X^2+X X^2+1 X X+1 X^2+X+1 X^2+X+1 1 1 X+1 X^2 0 1 0 X+1 X X^2 X 0 1 X 1 X X 1 0 X^2 X^2 X^2+X 0 X^2+X X^2 X^2+1 X^2+X+1 X+1 0 0 0 0 1 X 1 X+1 X+1 X+1 X 0 1 X^2+1 1 X^2+X X X+1 X^2+X X^2+X+1 X^2+X X^2+X+1 X X^2 1 X^2+1 X^2 X^2+X+1 X^2+X+1 0 X+1 X^2+X+1 1 X X^2+X X+1 X^2+1 X+1 X^2+1 0 1 1 0 X+1 X^2+X+1 1 X^2+X X^2 0 1 X+1 X^2+1 X^2+X+1 X+1 1 X^2 X^2 X^2+X+1 X^2+X X+1 X^2 X^2+X+1 X^2+X X^2+X+1 X+1 X^2+X+1 1 X^2 X^2+1 X^2+1 X^2+X 0 1 0 1 1 X^2+X+1 X^2 X^2+X X^2+1 1 0 X^2+1 X 0 X^2+X X^2+1 0 X^2 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 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 X^2 0 0 0 X^2 X^2 0 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 0 0 0 X^2 0 X^2 0 0 0 generates a code of length 88 over Z2[X]/(X^3) who´s minimum homogenous weight is 80. Homogenous weight enumerator: w(x)=1x^0+110x^80+274x^81+495x^82+566x^83+691x^84+660x^85+674x^86+652x^87+651x^88+418x^89+649x^90+468x^91+452x^92+362x^93+286x^94+256x^95+200x^96+88x^97+82x^98+62x^99+31x^100+18x^101+22x^102+12x^103+8x^104+4x^105 The gray image is a linear code over GF(2) with n=352, k=13 and d=160. This code was found by Heurico 1.11 in 1.67 seconds.