The generator matrix 1 0 0 0 0 1 1 1 0 1 X^2 1 X^2 1 X^2+X 1 0 1 1 X 1 1 X 1 0 0 1 1 1 1 X^2 X^2+X 1 0 X X^2+X 1 1 X^2+X 1 0 1 X 0 X^2 X^2+X X^2 1 X X^2+X 1 1 X^2 X^2 1 0 1 1 1 1 0 1 1 1 X 1 X 1 1 X X X 1 1 1 X^2 1 1 0 1 0 0 0 0 0 X^2 X^2 1 1 1 1 1 1 X+1 X^2+X X^2+X+1 X^2+X X X^2 X^2+X+1 1 X^2+1 1 1 X^2+X+1 X X^2+X+1 0 X 1 X X 1 1 X^2+X+1 0 0 X^2+1 1 X^2+X 1 0 X 0 1 X X^2 1 X^2+X+1 X^2 X X^2+X 1 1 X^2+1 X^2+X 0 1 X X^2+X+1 X 1 1 X+1 X^2 X^2+X X^2+1 1 X^2 1 X X X+1 X^2+X 0 0 0 0 1 0 0 X^2 1 X^2+1 1 0 1 X+1 X^2+X+1 X^2+1 0 X 1 X X^2+X+1 1 1 0 X X^2+1 X^2+X+1 1 0 X^2+X X^2+X+1 X^2+X 0 X X^2 X X^2 1 X X+1 X^2+X X^2+X+1 1 X^2+X+1 X^2+1 1 1 1 X X+1 1 X^2+1 X X^2+X X^2 X^2 0 X^2+X X X^2 X^2+X+1 X^2+1 X^2+X X+1 1 1 X^2 X^2+1 X^2+X X X^2+1 1 1 X^2+X+1 1 X^2+1 X^2+X+1 X^2+X X^2+X 0 0 0 0 1 0 X^2+1 1 0 1 X^2 X^2+1 X+1 X^2 X^2+X X^2+1 X^2+X+1 X^2+X 1 0 X^2+X+1 X+1 X^2 X+1 X^2+1 0 X+1 X^2+X X^2+X X^2 X^2+X+1 1 X+1 1 1 X^2+X X^2+X 0 X 1 X X^2+1 X^2+X+1 X X^2+X+1 0 X^2 1 X^2+X+1 X^2+X+1 X^2+1 X^2+1 0 X^2 X^2+X X^2+X+1 X X^2 X^2 X X 1 X^2+X X 1 X^2+1 X^2+X+1 1 0 X^2 X^2 1 X^2+X 1 X+1 X^2+1 X X^2+X 0 0 0 0 0 1 1 X^2 1 1 X^2+1 X^2 1 X+1 0 1 0 X^2+1 X+1 X^2+X X^2+X X^2+X+1 X^2+X 0 X^2+X X X+1 X^2+1 1 1 X 1 X^2+X+1 X^2+X+1 X^2 X+1 1 0 0 X+1 X^2+X X^2+X X X^2 X X^2+X+1 X^2 X^2+X+1 X^2 X^2 X^2+X+1 X^2+X X^2+X+1 1 1 X+1 1 1 X^2+1 X+1 X^2+1 X^2+X X^2+X+1 0 0 X^2 X X X+1 X X^2+X 1 0 X+1 X^2 X+1 1 1 0 generates a code of length 78 over Z2[X]/(X^3) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+104x^68+456x^69+843x^70+1086x^71+1413x^72+1734x^73+2069x^74+2162x^75+2643x^76+2550x^77+2799x^78+2556x^79+2723x^80+2232x^81+2087x^82+1576x^83+1275x^84+960x^85+603x^86+378x^87+245x^88+132x^89+70x^90+30x^91+8x^92+14x^93+5x^94+4x^95+4x^96+2x^97+4x^98 The gray image is a linear code over GF(2) with n=312, k=15 and d=136. This code was found by Heurico 1.13 in 16.6 seconds.