The generator matrix 1 0 1 1 1 X^2+X 1 1 0 X^2+X 1 1 1 1 X^2 1 X 1 1 1 X^2 X 1 1 1 X^2+X 1 0 1 1 0 1 0 1 1 1 0 1 1 1 X 1 X^2 X^2 1 1 X^2 1 1 X^2+X X^2+X 1 1 1 1 1 1 1 1 1 1 0 1 1 X^2+X 1 0 0 1 1 1 0 X 1 X X X^2 0 0 1 1 0 1 1 X X^2+X+1 1 1 X^2+X+1 X^2+X 1 X^2 1 0 1 X^2+1 1 X 1 1 X X+1 X^2+X+1 1 1 1 0 X 1 0 1 X 1 X^2+X+1 1 X^2+X X+1 0 1 0 1 1 X^2+X X^2 1 X^2+1 1 1 1 X 1 X^2+X+1 X^2+1 X^2+X X^2+1 0 X+1 0 X+1 1 X^2+X X^2+X+1 1 X^2+1 1 1 1 X^2 X X 1 X^2+1 X^2+X X X 1 0 0 X 0 0 0 0 0 0 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X X X^2+X X^2+X X X^2+X X^2+X X X^2+X X^2+X X^2+X X X X X^2+X X X X^2 X X X^2+X X^2 X^2 X X^2+X X X 0 X^2+X 0 0 0 X^2+X X X^2+X X^2 X^2 0 X 0 X X^2 X^2+X 0 0 X^2+X 0 X^2+X X^2+X X X^2 X^2 0 X^2+X X 0 0 0 X 0 0 X X^2 X X^2+X X X^2 X^2+X 0 X X^2+X X^2 X X^2 X^2 X^2 X^2+X X^2+X 0 0 X^2 0 0 0 X^2+X X^2+X X^2+X X X^2+X X^2+X X^2+X 0 X X X^2 X 0 X^2 0 X^2 X^2+X X X 0 X X^2 0 X 0 X^2 X X^2+X X^2 X X^2 0 X X X^2 0 X X^2 X^2+X X^2+X 0 X^2 X^2 X X^2+X X X X^2+X X^2+X 0 0 0 0 X 0 0 X X X^2+X X^2 X^2 X^2 X X^2 X X^2+X X^2+X X^2 X^2+X X^2+X 0 X X^2+X X^2 X X^2+X 0 X^2+X X^2+X X^2 X^2 X X^2+X X^2+X X X^2+X X^2 X^2 0 X^2+X X^2+X X^2 X 0 X^2+X X 0 X^2 0 0 0 X^2+X X^2 X X 0 X^2+X 0 0 0 X^2+X 0 X^2+X X^2+X X^2+X X^2+X X^2 X X^2+X X 0 X^2 0 X^2+X X X^2 0 0 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 generates a code of length 78 over Z2[X]/(X^3) who�s minimum homogenous weight is 69. Homogenous weight enumerator: w(x)=1x^0+86x^69+158x^70+282x^71+326x^72+440x^73+639x^74+630x^75+625x^76+654x^77+729x^78+656x^79+671x^80+564x^81+441x^82+456x^83+249x^84+190x^85+139x^86+58x^87+62x^88+40x^89+30x^90+26x^91+15x^92+6x^93+6x^94+4x^95+4x^97+2x^98+3x^100 The gray image is a linear code over GF(2) with n=312, k=13 and d=138. This code was found by Heurico 1.16 in 5.81 seconds.