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 X 1 X 0 X X X^2 X 0 X^2 1 X 1 0 0 1 1 0 1 1 0 1 X X^2 1 1 0 1 0 1 X 1 X 1 0 1 1 0 1 1 X X 1 X X X 1 0 X 0 X 0 0 X X^2+X 0 0 X X^2+X X^2 0 X^2+X X^2 X^2+X X^2 X X^2+X X X^2 X^2 X^2+X X^2 0 X^2+X X X^2+X X^2 X^2+X X^2+X 0 X^2+X X^2+X X^2+X X^2 X^2 X^2 X^2 X X X 0 X 0 X 0 0 X X 0 X X^2+X X X 0 0 X X^2+X X^2 0 X^2 X X X^2 X^2+X 0 X X X X^2+X X X^2+X X^2 X X 0 X X^2+X 0 0 0 0 X X 0 X^2+X X 0 0 X^2+X X 0 X X^2 X X^2 0 X^2+X X 0 X^2+X X X^2 X X^2+X 0 0 X^2 0 X^2+X X^2+X X X^2+X X^2 X^2+X X^2 X^2 X X X X X X^2+X X X X^2 X 0 X 0 0 X 0 0 X 0 X^2+X X X X X^2+X X 0 X X^2 X^2+X X X^2+X X^2+X 0 X^2 0 X X X^2+X 0 0 X^2 X X^2 X^2 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 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 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 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 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 0 0 X^2 0 0 0 0 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 0 X^2 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 0 0 0 0 X^2 X^2 0 0 0 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 X^2 0 generates a code of length 82 over Z2[X]/(X^3) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+59x^68+40x^69+135x^70+152x^71+278x^72+230x^73+313x^74+464x^75+620x^76+798x^77+884x^78+1100x^79+1102x^80+1280x^81+1427x^82+1294x^83+1158x^84+1246x^85+857x^86+768x^87+606x^88+374x^89+333x^90+268x^91+198x^92+106x^93+95x^94+44x^95+53x^96+20x^97+33x^98+6x^99+11x^100+2x^101+12x^102+8x^104+6x^106+2x^108+1x^110 The gray image is a linear code over GF(2) with n=328, k=14 and d=136. This code was found by Heurico 1.16 in 29.9 seconds.