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 0 X 1 X X X X^2 X X 0 1 1 0 1 0 X^2 1 0 1 X X 1 1 1 X^2 1 0 1 1 X 1 1 1 X X^2 X^2 X 1 1 1 0 X 0 0 0 X X^2+X X 0 X^2 X^2 X X^2+X 0 X^2+X X X^2 X^2+X X^2+X 0 0 X X^2+X X^2+X 0 0 X^2+X X X^2 0 0 X X X X 0 0 X X^2 X X X X^2 0 X^2 X X X^2+X X X X X^2 X^2 X X X^2 X^2 X X X^2+X 0 0 0 0 X X 0 0 X X^2 X^2 X 0 X X^2 X^2 X X^2 0 0 0 X 0 X X X^2+X 0 0 0 X X^2 X X^2+X X^2 X^2+X X^2 X^2 X^2 0 X X X^2 X^2+X X^2 X X X^2 X X^2+X 0 X X^2+X X^2+X X^2+X 0 X X^2+X X X^2 X X^2+X 0 X^2+X X^2 X 0 X^2 0 0 X^2 X^2 X^2 X^2 X 0 X^2 X X^2 X^2+X 0 X^2 X 0 X^2 X^2+X X^2+X X X^2+X X X X^2+X X X^2+X X X X^2+X X^2 0 0 0 0 X X 0 X^2+X X 0 X 0 X X^2+X X^2+X X^2 X^2 0 X^2 X X^2+X 0 0 X^2+X X^2+X X 0 X 0 X X 0 0 X^2 X^2 X X^2 X^2 0 X 0 X^2 X X X^2 X^2+X X^2 X^2+X X^2 0 X^2 X^2+X X X X^2 0 0 X X X 0 X^2+X X^2+X X X X^2+X X X 0 X X X^2+X X X^2+X X^2+X X^2 0 X 0 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 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 0 0 0 X^2 X^2 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 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 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 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0 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 X^2 0 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 0 0 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 generates a code of length 79 over Z2[X]/(X^3) who´s minimum homogenous weight is 66. Homogenous weight enumerator: w(x)=1x^0+55x^66+74x^67+175x^68+192x^69+299x^70+350x^71+476x^72+570x^73+723x^74+930x^75+1072x^76+1238x^77+1327x^78+1444x^79+1327x^80+1366x^81+1123x^82+894x^83+690x^84+532x^85+381x^86+326x^87+238x^88+158x^89+143x^90+70x^91+100x^92+38x^93+33x^94+8x^95+10x^96+2x^97+11x^98+3x^100+4x^104+1x^114 The gray image is a linear code over GF(2) with n=316, k=14 and d=132. This code was found by Heurico 1.16 in 26.6 seconds.