The generator matrix 1 0 1 1 1 X^2+X 1 1 0 1 1 X^2+X 1 X^2+X 1 1 0 1 0 1 1 1 X^2+X 1 1 0 1 X^2+X 1 1 1 1 0 1 0 1 1 1 X^2+X X^2+X 1 1 0 1 1 0 1 1 X^2 1 1 1 X^2+X 1 X^2+X 0 1 1 X 1 1 1 1 1 1 1 1 X^2 1 1 0 0 X 1 1 1 1 0 1 X+1 X^2+X 1 1 0 X+1 1 X^2+X X^2+1 1 X^2+X 1 X+1 0 1 X^2+1 1 X^2+1 0 X^2+X 1 X+1 X^2+X+1 1 0 1 X^2+X X^2+1 X+1 0 1 X^2+X 1 X^2+1 X^2+X X+1 1 1 0 X^2+1 1 X^2+X X^2 1 X+1 X^2+1 1 X^2+X X+1 X 1 X+1 1 1 X^2+1 X+1 1 X 0 X^2+1 1 X^2+X 0 X^2 X^2+X+1 1 X^2+X X+1 0 1 X^2+X X^2+X X^2+X+1 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 0 0 0 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 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 0 0 0 0 X^2 0 0 0 0 0 0 X^2 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 0 X^2 0 X^2 0 X^2 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 0 0 0 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 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 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 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 0 X^2 0 0 X^2 0 X^2 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 0 0 X^2 0 0 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 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 0 0 0 0 0 0 0 0 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 0 0 0 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 generates a code of length 77 over Z2[X]/(X^3) who´s minimum homogenous weight is 64. Homogenous weight enumerator: w(x)=1x^0+84x^64+54x^66+36x^67+373x^68+196x^69+476x^70+408x^71+1032x^72+744x^73+1292x^74+1096x^75+1880x^76+1192x^77+1736x^78+1072x^79+1454x^80+752x^81+862x^82+436x^83+550x^84+180x^85+172x^86+24x^87+170x^88+8x^89+16x^90+56x^92+25x^96+5x^100+2x^104 The gray image is a linear code over GF(2) with n=308, k=14 and d=128. This code was found by Heurico 1.16 in 19 seconds.