The generator matrix 1 0 1 1 1 X^2+X 1 1 X^2 1 X 1 1 1 0 0 1 1 X^2+X 1 1 1 1 X X^2+X 1 1 1 0 1 1 1 1 X^2 X^2+X X 1 1 1 1 X^2 1 X^2+X 1 X 1 X^2+X X^2+X 1 1 1 1 1 X X 1 1 1 1 1 1 1 X^2+X X^2 1 1 X X^2 X^2+X X 1 1 X X^2 X 1 0 1 1 0 X^2+X+1 1 X+1 X^2+X 1 X^2 1 X^2+1 X X+1 1 1 0 X^2+1 1 X^2+X+1 X^2+X X^2+1 X^2+X 1 1 X^2+X+1 X^2+X 1 1 0 X^2 X^2 X^2+1 1 1 1 X^2+1 X+1 X^2+X 0 1 X 1 X^2+X 1 X^2+X 1 1 X X^2+X X^2+1 1 X+1 1 1 X^2+1 X^2+X+1 X^2+X+1 X X^2+X 0 X^2 1 1 0 X^2+1 1 1 1 X^2 X X+1 1 1 0 0 0 0 X 0 X^2+X 0 X^2 X^2 X X^2+X X^2+X X^2 X X X 0 X X^2 X^2+X X^2 X X^2+X 0 X^2 X^2+X X^2+X X^2 X^2 0 X 0 0 X^2 X^2+X X 0 0 X^2+X 0 0 0 X^2+X X^2+X X^2+X 0 0 X^2 X^2+X 0 X^2+X X X X^2 X 0 X^2 0 X X^2+X X^2+X X^2 X^2+X X X^2 X^2+X 0 X X X^2+X X^2+X X^2 X^2 0 X^2 0 0 0 0 0 X 0 0 0 X^2 X^2 X^2 X^2 0 0 X X X X^2+X X X X X X^2+X X^2+X X^2+X X^2 X 0 X X 0 0 X^2+X X^2 0 X^2+X X^2 X^2 X^2 0 0 X^2+X X^2+X X X 0 X^2+X X^2 0 X^2+X X^2 0 X X^2 X^2+X X^2+X X X^2+X X^2+X 0 X^2 X^2+X X^2+X X^2 0 X^2 X X X^2 X^2 X X^2 X^2+X X^2+X X X^2+X 0 0 0 0 0 X^2 0 0 0 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 generates a code of length 76 over Z2[X]/(X^3) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+48x^68+152x^69+177x^70+234x^71+299x^72+360x^73+352x^74+330x^75+371x^76+348x^77+328x^78+214x^79+247x^80+248x^81+129x^82+98x^83+45x^84+30x^85+24x^86+10x^87+8x^88+12x^89+10x^90+8x^91+4x^92+2x^93+3x^94+2x^95+1x^96+1x^106 The gray image is a linear code over GF(2) with n=304, k=12 and d=136. This code was found by Heurico 1.16 in 1.27 seconds.