The generator matrix 1 0 0 1 1 1 X 1 X^2+X 1 1 X 1 X^2+X 1 X^2+X 1 1 0 0 1 1 X^2 1 1 0 1 1 X^2+X 1 X^2 X^2 X 0 1 1 1 1 1 X 1 X^2 1 X^2 1 X 1 1 X^2+X 1 X 1 1 0 X^2 1 1 1 1 0 1 1 X^2 X^2+X X^2+X 1 1 1 1 X^2 0 1 X^2 1 X 0 1 0 1 0 0 1 X^2+X+1 1 X^2 0 X^2 X^2+X+1 1 X+1 1 0 1 X^2 X^2+X 1 1 X^2+X+1 X^2+X+1 X 1 X^2+X 1 X^2+X+1 1 0 X^2 1 X 1 1 X^2+X X^2+X+1 X X^2+X+1 X+1 0 X^2+X 1 X^2+X+1 1 X 1 0 X^2+X 1 X^2+X 1 1 X^2 1 1 X+1 X^2 X X^2+X+1 X X^2+X+1 X^2 X 1 0 0 X^2+1 X+1 0 0 1 X^2+X+1 X^2 0 1 1 1 0 0 1 1 X+1 0 1 X+1 1 X X+1 X X X+1 X+1 X^2+1 X X^2+X+1 0 1 X^2+1 X^2 1 X^2 X^2+X X X^2+X+1 X^2+X 1 X^2 X+1 1 0 X^2 X+1 X X^2+X+1 X+1 X 1 X^2+1 X^2+X+1 X^2+1 X^2+X 1 X^2+X+1 0 0 X^2+X X^2 X^2 X^2 X^2 X+1 X+1 X^2+X+1 X^2 X^2+1 X^2+X 1 X^2 X^2+1 1 X^2+X+1 1 1 X^2+1 X^2+1 X^2+X+1 1 1 X^2 1 X^2 X^2+1 X^2+1 1 0 0 0 X X X^2+X X^2 X^2+X 0 0 X X^2 X 0 X^2 X^2+X X X^2 X^2+X X 0 X^2 X 0 X^2+X X^2+X X^2 X X^2+X X 0 X^2 X X^2+X 0 X^2 X^2+X X X^2+X X^2+X X^2 X X^2+X X^2 X X X^2+X X^2+X X 0 0 X^2 X^2 X^2 0 X^2 X^2+X 0 X X^2 X^2 X^2+X X X X X X X^2 X X X^2 X X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 0 0 0 0 0 0 X^2 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 X^2 X^2 0 0 0 0 0 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 0 X^2 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 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 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 0 generates a code of length 77 over Z2[X]/(X^3) who´s minimum homogenous weight is 69. Homogenous weight enumerator: w(x)=1x^0+90x^69+282x^70+356x^71+618x^72+534x^73+747x^74+630x^75+761x^76+592x^77+734x^78+512x^79+643x^80+376x^81+410x^82+244x^83+236x^84+182x^85+118x^86+38x^87+34x^88+12x^89+11x^90+10x^91+11x^92+4x^93+2x^94+2x^95+2x^97 The gray image is a linear code over GF(2) with n=308, k=13 and d=138. This code was found by Heurico 1.16 in 3.92 seconds.