The generator matrix 1 0 0 1 1 1 0 1 X X^2 1 1 X 1 X^2+X X^2 X^2+X 1 1 1 1 X 1 1 0 1 X^2+X X^2+X 1 1 1 1 X^2 X 1 1 1 0 1 1 1 0 1 1 1 X^2 1 X^2+X X^2 1 1 1 1 X^2 1 X^2 X X^2 1 X^2+X 1 1 1 X^2+X 0 X^2 X X^2 1 X^2 X^2+X X^2 1 1 1 X^2 1 1 1 X^2 X X 1 1 X^2 1 0 1 0 0 1 1 1 X 1 X^2+X 1 X^2+X 1 X+1 X^2 1 1 X^2+1 X^2 X^2+X+1 X 1 0 X+1 1 X 1 X^2+X X+1 X^2+X X^2+1 X X^2+X 1 X^2+1 X 1 1 X^2+1 0 X^2+X+1 1 X^2+X+1 X^2+X X^2 X^2 X^2+X+1 1 1 X^2+X+1 X^2 0 X 1 X^2+1 X^2 0 1 X 1 X+1 X+1 X 1 1 1 1 X X^2+1 1 1 1 1 1 X^2+X X^2+X X+1 X+1 X^2+X X^2 1 X^2 X+1 X^2 1 X^2+1 0 0 1 X+1 X^2+X+1 0 X+1 1 X^2 1 X^2+1 0 1 X 1 X X+1 X X^2+1 X^2+1 X^2+X X X X+1 X+1 1 X^2+X+1 1 0 X+1 X^2 X^2+X 1 X^2+X X+1 0 1 X^2 X X^2 X^2+X+1 1 0 X^2+1 X^2+X 1 1 X^2+1 X 0 1 X^2+X+1 X^2 X^2+1 X 1 1 0 X^2+X+1 X^2+X X^2 X^2+X X^2 X+1 X X+1 X^2 1 0 X^2+1 X^2+X+1 X^2+1 X^2+1 X^2+1 X^2+X+1 1 1 1 X^2 1 X^2+X+1 1 X X^2+X X^2 X^2+X 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 0 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 0 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 0 0 0 X^2 X^2 0 0 0 0 X^2 X^2 0 0 0 generates a code of length 86 over Z2[X]/(X^3) who´s minimum homogenous weight is 80. Homogenous weight enumerator: w(x)=1x^0+440x^80+684x^82+892x^84+584x^86+565x^88+356x^90+266x^92+132x^94+95x^96+32x^98+42x^100+4x^102+3x^104 The gray image is a linear code over GF(2) with n=344, k=12 and d=160. This code was found by Heurico 1.16 in 35.8 seconds.