The generator matrix 1 0 0 1 1 1 X^2+X X 1 1 1 X^2 1 X^2 0 1 1 1 X 0 1 X^2 X^2+X 1 1 1 1 X X^2+X 1 X^2 1 X 1 1 X^2 0 1 0 1 1 1 0 1 1 1 1 1 X 1 1 X^2+X 1 X 0 1 1 0 1 0 1 X X^2+X 1 X 0 1 1 1 X^2 X^2+X X^2+X 1 1 1 X^2 1 0 X 1 1 1 1 0 X^2 X^2+X 0 0 1 0 0 1 X+1 1 X^2 X^2+X+1 X+1 X^2+X 1 X^2 1 0 0 X^2+1 X 1 1 1 1 0 X X^2+X+1 X^2+1 X^2+X 1 X 1 1 X^2+X 1 X 1 1 1 X^2+X 1 X^2 1 X^2+1 X^2+X X^2+1 X X^2 X^2 X^2 1 X^2 0 1 X^2 X^2 1 X X^2+X+1 1 X^2+1 1 X+1 1 1 X+1 1 1 X X^2+X+1 0 1 1 1 X X^2+X X+1 1 X^2 1 X^2 X^2 X^2+1 0 X^2+X+1 X X^2 X^2+X 1 0 0 1 1 1 X^2 1 1 X+1 X^2+X X^2+1 X^2+X X X^2+1 1 X^2 1 1 1 X^2 X^2 1 1 X+1 X^2+X X^2+X+1 X^2 0 1 0 X+1 X^2 X^2 X+1 X^2+X+1 X^2+X+1 X X^2+X X^2 X^2+X X X^2 1 X^2+1 X^2+X X^2+1 1 X^2+X+1 1 1 X^2+X X X^2+X 1 X+1 X^2+1 X^2+1 X X^2+X X X X^2+X X+1 0 X^2+X+1 X+1 X^2+1 X+1 X+1 0 X^2 X^2+X X^2+1 X+1 X^2 X^2+1 X^2+X+1 X^2+X 1 X^2+X+1 X^2+1 1 1 1 1 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^2+X X^2+X X^2 0 X^2 X^2+X X X^2 0 0 X^2 X^2 X X X^2 X^2 X X^2 0 X X^2+X 0 0 X 0 X X^2+X X^2+X X^2+X X^2 X^2 X^2 X^2+X X 0 0 X^2 X^2+X X^2+X X X^2+X 0 X X 0 X^2+X X X X X^2+X X X^2 X^2 X^2 0 X^2 X^2+X 0 0 X^2+X X^2 0 X^2+X X^2 X^2 0 X X^2+X X^2+X X^2+X X X X^2 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 0 0 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 0 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+80x^80+240x^81+290x^82+362x^83+419x^84+390x^85+359x^86+308x^87+302x^88+266x^89+233x^90+160x^91+152x^92+148x^93+75x^94+114x^95+73x^96+36x^97+45x^98+14x^99+13x^100+6x^101+4x^102+2x^105+2x^110+2x^111 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 1.42 seconds.