The generator matrix 1 0 0 0 1 1 1 1 X X^2+X X 1 X^2 1 1 0 1 1 X^2 1 1 1 X 0 1 1 1 X^2 X 0 1 1 0 1 X^2+X X^2 X^2 1 X^2+X X 1 X 1 X 1 X 0 1 1 X^2 1 1 X^2 1 0 X 1 1 1 X^2+X X^2 1 X 1 1 X^2+X 1 X^2+X 1 0 X^2+X X X^2 X 1 0 X^2+X X^2+X 1 X^2+X X X 0 X^2 1 1 0 1 0 0 X X X^2+X X+1 X^2+X 1 1 X^2+X+1 1 X^2+X+1 X+1 0 X^2 1 X 1 X^2 X^2+X 1 X X^2+1 X^2+X X^2+1 1 1 1 1 0 1 0 1 1 X X^2+X X^2 1 X+1 0 X 1 1 X X^2 X+1 0 0 X 0 1 X^2+X+1 1 1 1 X^2+X X+1 X^2+X 1 X^2+X X^2 0 1 1 X^2+X+1 1 1 1 X^2+X X^2+X 1 1 X^2+1 1 1 X^2 1 1 1 0 X^2 1 X X^2 0 0 1 0 X X^2+X+1 X^2+X+1 X+1 1 X^2+X X+1 X^2+X X^2+1 X^2+1 X^2 1 X 0 X 0 X^2+X 1 X+1 1 X+1 X+1 1 1 X^2+X X^2 X^2+X X^2+X+1 X^2+X X^2 X^2+1 X^2+X 1 X 1 X^2+X X^2+1 1 0 1 X^2 1 1 1 X+1 X^2+X 0 0 0 X+1 X+1 1 X^2+1 X^2 1 1 0 1 X X^2+X+1 X X 1 0 1 1 1 X^2 X^2+X+1 X+1 X+1 X^2+X X X^2 X^2+X+1 X^2+X+1 X+1 X^2+X 1 0 X+1 X^2 0 0 0 1 X+1 X^2+X+1 X X^2+X+1 X^2+X+1 X+1 X^2+X X^2+X 1 0 X^2+X+1 X^2+X X^2+1 X 1 X^2+1 X^2 1 X^2+X+1 X^2+X+1 X^2+X X^2 X+1 X^2+X X^2+1 X^2+X X+1 1 1 1 0 X^2 1 0 X^2 0 0 1 1 X^2+X X^2 X X X^2+1 X^2+1 1 X+1 X^2 X+1 X^2+X+1 X+1 X^2 0 X+1 X+1 1 1 X+1 1 0 X^2+X+1 1 X X 1 X+1 X^2 1 X^2+X X^2+1 1 X+1 X^2 1 0 X^2+X X^2+X+1 1 X^2+1 0 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 0 0 X^2 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 0 generates a code of length 86 over Z2[X]/(X^3) who´s minimum homogenous weight is 78. Homogenous weight enumerator: w(x)=1x^0+104x^78+282x^79+510x^80+568x^81+604x^82+700x^83+625x^84+614x^85+672x^86+616x^87+550x^88+536x^89+416x^90+356x^91+262x^92+254x^93+218x^94+110x^95+75x^96+30x^97+24x^98+16x^99+21x^100+12x^101+10x^102+4x^104+2x^105 The gray image is a linear code over GF(2) with n=344, k=13 and d=156. This code was found by Heurico 1.16 in 4.59 seconds.