The generator matrix 1 0 1 1 1 X^2 1 1 0 1 1 0 1 1 X^2 1 1 X^2 1 X^2 1 X 1 1 1 1 X^2+X 1 1 X^2+X 1 X 1 1 1 X^2+X 1 X^2 X^2 1 1 1 1 X^2 1 X^2+X 1 1 1 X^2 1 X^2+X 1 X^2 1 1 1 1 1 1 X^2+X 1 1 1 1 X^2+X 1 1 1 X X 1 1 X^2+X 1 X X^2+X X^2+X 1 1 1 0 1 X 1 0 1 1 0 1 1 X^2 X+1 1 1 0 1 X+1 0 1 X+1 0 1 X+1 1 0 1 0 X^2+1 X^2 X^2+X+1 1 X+1 X^2+X 1 X+1 1 X X X^2+X+1 1 X 1 1 X^2 0 X^2+X 1 1 X^2+1 1 X X^2+X X^2+X+1 1 1 1 X^2+X+1 1 X^2+X+1 1 X^2 1 0 X^2+X 1 X^2+X+1 X X^2+X+1 0 1 X+1 1 X+1 X X^2+X 1 X^2+1 1 X 1 1 1 X^2+X+1 X X^2+X 0 X^2+X 1 X^2+X 0 0 X 0 0 0 0 0 0 0 0 0 0 X^2+X X^2+X X X X^2+X X^2+X X X^2+X X^2+X X^2+X X X^2 X^2 X^2+X X^2 X X^2 X^2 X^2 X X^2+X X^2+X X X X^2+X X^2 X X^2 X^2 X^2 X X^2+X X^2 0 X^2 X^2+X X^2 X X^2+X X^2 X^2 X^2 X^2 X^2 X^2 X X^2 X X^2 X X^2+X X 0 0 X^2 X X^2+X 0 X^2+X X X^2+X 0 0 X^2+X X^2+X X X^2+X 0 0 X^2+X 0 X^2+X 0 0 0 X 0 0 X^2 X^2 X^2+X X^2+X X X X^2+X X^2 X X^2 X^2+X X X X^2 X^2+X X^2 0 X^2+X X X X 0 X^2 X^2 X^2+X 0 X X X^2 0 X^2 X^2+X X 0 X^2 X^2 X^2+X 0 0 X^2+X X^2+X X 0 X X X^2 0 0 0 X X^2+X X^2+X X^2+X X^2 X 0 0 X^2+X X X X X^2+X X 0 X^2 X^2+X X^2 X^2 X^2 0 X^2+X X^2+X 0 0 X^2 X X^2 0 X 0 0 0 0 X X^2+X X^2+X 0 X X^2 X X^2 X^2+X X^2+X X^2+X X^2+X X^2 0 X^2 X X X^2 0 X^2+X X^2 0 X^2 X^2+X X X^2+X X^2+X X^2 X 0 0 X^2 X^2 X^2+X X^2 X X 0 0 X^2+X X X X X^2 X^2+X 0 X X X X X^2 X^2+X X X^2+X 0 X^2+X X^2+X 0 X^2+X 0 0 0 X^2 X X^2 X^2+X X^2+X X^2+X X^2 X^2+X 0 X^2 0 X^2+X 0 0 X^2 0 X X X^2+X 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+260x^78+621x^80+604x^82+669x^84+624x^86+557x^88+420x^90+193x^92+74x^94+22x^96+16x^98+8x^100+14x^102+6x^104+4x^106+2x^108+1x^112 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 26.3 seconds.