The generator matrix 1 0 0 1 1 1 X^2+X 1 X 1 1 1 0 X 0 X 1 1 1 0 1 X 0 0 1 1 1 1 1 0 1 1 X X^2 1 0 1 X^2 1 1 1 1 1 X^2+X X^2 1 X 1 1 1 X^2 1 1 X 1 1 X X^2+X 1 1 0 1 1 1 0 X^2 1 1 X^2 1 1 1 0 1 X^2 X 1 1 1 1 X^2+X X^2+X 1 X^2+X 1 0 X^2 1 0 0 1 0 0 1 X+1 1 X^2+X 0 X+1 X^2+X 1 1 1 X^2+X 1 X^2+1 X^2+X+1 0 1 X^2+X 1 1 X^2 X^2+1 X^2+X X^2+1 X X+1 1 X+1 0 X^2+X 1 X^2 1 X+1 X^2+X X^2 X^2+X+1 0 X X^2+X+1 1 1 X^2+X+1 1 X^2+X X^2+X+1 X^2 1 X^2+X+1 X^2+X+1 1 X X+1 X^2 1 0 0 1 X X X^2 X^2+X 0 X^2+X+1 X X^2 X^2 X^2+X X^2+1 X X+1 1 1 X^2+1 X+1 X^2+X+1 X 0 0 X^2 1 X^2+X X^2 0 X^2+1 1 0 0 1 1 1 0 1 1 1 X^2+1 0 X^2 1 X^2 1 X^2+X X^2+X X+1 X^2+X 1 X^2+1 X^2+X+1 0 1 0 X^2+1 X^2+1 0 X 1 X^2+1 X^2+X+1 1 1 0 X^2+X X^2+X+1 1 X+1 X X X+1 X^2+X+1 X X+1 0 X^2+X+1 X^2 X X+1 X X^2+X X^2+X+1 X X^2+X X^2+1 1 X+1 X+1 X^2+X X^2+X X^2+X X^2+1 1 1 1 X^2+1 X^2+X+1 1 1 X^2 X+1 1 X^2+1 1 0 X^2 X+1 X^2 0 1 1 X X^2+X X^2 1 1 X+1 X 0 0 0 X 0 0 X^2 X^2 X^2 X^2+X X X X^2+X X X 0 X^2+X X^2 X 0 0 X^2+X X X^2+X 0 X^2+X X 0 X X^2 0 X^2+X X^2 X^2+X X X^2 X X^2 X^2+X 0 X^2 0 X X^2+X X^2+X X^2 X^2+X X^2 X^2+X 0 X^2 X^2+X 0 X^2 X^2+X 0 X^2 X^2 X^2 X^2+X 0 X X X^2 X^2+X X^2 0 X X^2+X 0 X^2+X X 0 X^2 X^2 X^2+X X^2+X X^2 X X^2 X^2+X 0 X^2 X^2+X 0 X^2 0 X^2+X X^2 0 0 0 0 X X^2 X X^2+X X^2+X X^2 X X^2+X 0 X 0 X^2+X X^2 0 X^2 X^2 X^2 X X^2 X X^2+X X^2+X X^2+X X X^2+X X X^2+X X^2 X X 0 0 X X^2 X X^2 X^2+X X^2+X X^2 X^2+X X^2+X X^2+X 0 0 X^2+X X X^2+X X^2 X X^2 X 0 X X^2 X^2 X X X^2 0 0 X X X X X^2+X X^2 0 X^2+X X X^2+X 0 X^2 0 X^2 X^2+X X^2 X^2 0 X^2 0 0 X^2 X^2+X X^2 X generates a code of length 89 over Z2[X]/(X^3) who´s minimum homogenous weight is 81. Homogenous weight enumerator: w(x)=1x^0+142x^81+368x^82+394x^83+615x^84+568x^85+709x^86+496x^87+778x^88+590x^89+630x^90+480x^91+600x^92+352x^93+435x^94+282x^95+251x^96+142x^97+130x^98+96x^99+53x^100+24x^101+27x^102+6x^103+6x^104+2x^105+4x^106+6x^107+1x^110+4x^113 The gray image is a linear code over GF(2) with n=356, k=13 and d=162. This code was found by Heurico 1.16 in 5.77 seconds.