The generator matrix 1 0 1 1 1 X^2+X 1 1 0 X^2+X 1 1 1 X^2 1 1 1 0 X 1 1 1 1 X 1 1 1 X X 1 X^2 1 X^2 1 1 X^2 X 1 1 1 1 1 1 X^2 1 X^2 1 1 1 X^2+X 1 1 X^2+X 0 1 1 1 1 X^2+X 0 X^2 X 1 1 1 X^2 X^2 1 1 1 X^2 0 1 X 1 1 1 0 1 1 0 1 1 X X^2+X+1 1 1 X^2+X+1 X^2+X 1 1 0 X X^2+1 1 1 X+1 1 X^2+X+1 X^2+X 1 X^2 0 X^2+X 1 1 X 1 X^2+1 1 X+1 X 1 1 X X X+1 0 X^2+1 X+1 1 X^2 1 1 X X 1 X^2+1 X 1 1 X^2+X X^2+1 1 X 1 1 1 1 0 X^2 X 1 X 1 X 1 1 1 X^2+X 1 X X+1 X+1 0 0 X 0 0 0 0 0 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 0 X X X X^2+X X X X X X^2+X X^2+X X X^2+X X^2+X X^2+X X^2+X X^2+X X^2 X X X^2 X X X^2 X^2 X^2 0 X^2 X X^2+X X^2+X X^2+X X X X^2+X X X^2 X 0 X X X 0 0 X X^2 X X^2 X^2 X X^2 0 X^2 0 0 0 0 X 0 0 X X^2 X X^2+X X X^2 X^2+X X X X^2 X^2 X^2 0 X X X^2 X X^2+X 0 X^2+X 0 0 0 X^2+X X^2+X X 0 X^2+X X^2 0 X^2+X X X^2+X 0 0 X 0 X^2+X X^2 X^2 X X X^2 X^2+X X X 0 X^2+X 0 X X X X^2+X X X^2 X X^2 0 X^2 0 X^2+X 0 X^2 X^2+X X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 X 0 0 X X X^2+X X^2 X^2 X^2 X^2 X^2+X X^2+X X^2 X^2+X X^2+X X^2+X X 0 X^2+X X^2 0 X X^2+X X^2 X 0 X 0 X X X^2 0 X^2+X X 0 X^2 X^2+X X^2+X X 0 0 0 X^2+X X^2+X X X X^2 X 0 X^2+X X X^2 X^2 0 0 X X X^2 X 0 0 X^2+X X^2 X^2 X^2 0 X X^2+X 0 X X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 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 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 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 0 0 X^2 X^2 0 0 0 0 X^2 generates a code of length 77 over Z2[X]/(X^3) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+76x^68+162x^69+195x^70+398x^71+413x^72+572x^73+677x^74+672x^75+727x^76+632x^77+730x^78+596x^79+626x^80+558x^81+370x^82+274x^83+154x^84+122x^85+55x^86+64x^87+41x^88+28x^89+19x^90+6x^91+6x^92+4x^93+6x^95+3x^96+2x^97+2x^98+1x^108 The gray image is a linear code over GF(2) with n=308, k=13 and d=136. This code was found by Heurico 1.16 in 5.46 seconds.