The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 X 1 1 1 X X X X X X X 1 1 X^2 X 1 X 1 1 X X X^2 X 1 1 1 1 1 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 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 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 0 0 X^2 0 0 0 X^2 0 X^2 0 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 0 X^2 0 0 0 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 0 0 X^2 0 0 X^2 0 0 X^2 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 0 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 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 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 0 X^2 0 0 X^2 0 X^2 0 0 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 0 0 0 X^2 0 0 X^2 0 X^2 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 0 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 0 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 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 68. Homogenous weight enumerator: w(x)=1x^0+125x^68+344x^72+8x^74+525x^76+118x^78+774x^80+482x^82+3388x^84+4924x^86+3310x^88+492x^90+842x^92+110x^94+469x^96+10x^98+289x^100+118x^104+44x^108+8x^112+2x^116+1x^140 The gray image is a linear code over GF(2) with n=344, k=14 and d=136. This code was found by Heurico 1.16 in 38.5 seconds.