The generator matrix 1 0 0 1 1 1 X^2+X X 1 1 1 X^2 1 X 0 1 1 X 1 0 1 1 X^2+X 1 X^2+X 1 X 1 X^2+X 1 0 1 X X^2 1 0 X X^2+X 1 1 1 1 1 X 1 X^2 X^2 1 1 0 1 0 1 X 1 1 1 0 1 X^2 X^2 1 0 1 1 X X 1 1 1 1 1 X^2 0 1 0 X X 1 0 1 1 X^2+X 1 1 0 1 0 0 1 X+1 1 X^2 X^2+X+1 X+1 X^2+X 1 X^2 1 X^2 X^2+X X+1 1 X+1 1 X^2 X+1 X^2 X^2 1 X 1 X+1 1 X^2+X X^2+X X^2 1 1 X+1 1 0 1 X X^2+X X^2+X+1 X^2 X+1 X^2 X^2+X 1 1 X 1 1 X^2 1 X^2 1 X X^2+1 X^2 1 X 1 1 X+1 1 X^2+X+1 0 1 0 X^2+X X^2 1 X^2+1 X 1 1 X^2+X 1 1 1 1 X 1 X^2+X X X^2+X+1 X^2 0 0 1 1 1 X^2 1 1 X+1 X^2+X X^2+1 X^2+X X X+1 1 X^2+X+1 1 X^2+X X^2 X+1 X^2+X 1 1 X+1 1 0 0 X^2 X^2 X^2+X+1 1 X^2+X 1 X^2 X^2+X 1 1 X+1 1 1 X^2+X+1 X^2 X^2 1 X^2+X+1 X^2+X+1 0 X^2 X^2 X X^2+X+1 X^2+X X^2+1 X X^2+1 X^2 X^2+X+1 1 X^2+X+1 X^2+1 X X+1 X^2+1 X^2+1 X^2 X 1 X^2+1 0 1 0 X^2+1 X^2+X+1 X^2+X+1 X^2+1 X X^2 X^2+X X^2+1 1 X^2+X+1 X^2+X 1 X^2+1 X^2 0 0 0 X X^2+X 0 X X X^2+X 0 X^2+X 0 0 X^2+X X X X X^2 X^2+X 0 X X^2 X^2 X^2 0 X X^2+X X X^2 0 X^2 0 X X^2+X X^2+X X^2+X 0 X^2 0 X 0 X^2+X X^2 X X^2+X X X^2 X^2 X X X^2+X X^2+X X^2 X^2+X X^2 X^2+X X X^2 X^2 0 X^2 X^2 X X X^2 X^2 X^2+X 0 X^2+X X^2 X X^2+X X X^2+X X 0 X^2+X 0 X^2 0 X^2+X 0 X^2 0 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 0 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 0 0 0 0 0 generates a code of length 85 over Z2[X]/(X^3) who´s minimum homogenous weight is 78. Homogenous weight enumerator: w(x)=1x^0+80x^78+250x^79+279x^80+416x^81+330x^82+390x^83+351x^84+400x^85+204x^86+266x^87+185x^88+294x^89+159x^90+146x^91+93x^92+62x^93+66x^94+60x^95+23x^96+10x^97+7x^98+8x^99+8x^100+2x^101+1x^102+4x^104+1x^110 The gray image is a linear code over GF(2) with n=340, k=12 and d=156. This code was found by Heurico 1.16 in 1.36 seconds.