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 X 0 X 0 X 0 1 X 0 1 1 X 1 0 X 1 0 1 1 1 0 1 1 X 1 1 0 X 1 1 0 X 1 1 0 1 X^2 X 0 1 1 1 1 1 X^2 X X^2 1 1 0 1 0 X 0 X^2+X 0 X^2+X 0 X^2+X 0 X^2+X 0 X^2+X X^2+X X^2 0 X^2+X X X^2 X^2+X X^2+X X 0 0 X^2 0 0 X^2+X X^2+X 0 X^2 X X^2+X X X^2+X X X^2+X X X X^2+X X X^2+X X^2+X X^2+X 0 X X^2+X X^2 X X 0 X X 0 X^2 X^2+X X 0 X X^2+X 0 0 X X^2+X X^2 X X X^2+X X^2 X X X^2 0 X 0 0 X X^2 X X^2 X^2+X X X^2+X 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 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 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 0 0 X^2 0 0 0 0 X^2 0 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 0 0 0 X^2 0 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 0 X^2 X^2 0 0 0 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 X^2 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 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 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 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 0 X^2 0 0 X^2 0 0 X^2 0 X^2 0 0 0 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 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 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 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 0 X^2 X^2 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 X^2 0 0 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 0 0 0 0 X^2 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 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 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 0 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 0 X^2 X^2 0 0 X^2 X^2 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 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 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 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+154x^68+58x^70+12x^71+533x^72+84x^73+346x^74+244x^75+858x^76+796x^77+708x^78+1304x^79+1051x^80+1576x^81+852x^82+1800x^83+1049x^84+1304x^85+706x^86+668x^87+852x^88+324x^89+338x^90+68x^91+379x^92+12x^93+64x^94+167x^96+53x^100+19x^104+3x^108+1x^112 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 32.2 seconds.