The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X^2 1 1 0 X^2 1 1 1 0 1 X 1 1 1 0 1 X X 1 X 1 X 1 X X^2 X 1 0 0 1 1 0 X 0 X 0 0 X X^2+X 0 X^2 X X^2+X 0 X^2+X X^2 X^2+X X 0 X^2 X X^2 X^2+X 0 X^2+X 0 X^2 X X X^2 0 X X 0 X^2 X X^2+X 0 X^2 0 0 X X X^2+X X X^2+X X 0 X^2 X X X^2 0 X^2+X X 0 0 X X^2 X^2 0 X^2+X X X 0 X^2 X^2 X X^2 X X X^2 0 X X X^2+X 0 0 0 X X 0 X^2+X X 0 X^2 X X 0 X^2 X^2+X X X^2 X 0 X^2+X 0 0 X^2 X^2+X X 0 X X X^2 0 X^2+X X^2+X X^2 0 X X 0 0 X^2+X X^2+X X^2 X X^2 X^2+X X^2+X 0 X^2+X X X X^2 X^2+X X^2 X^2+X X^2 0 X X^2+X X^2+X X X^2+X X X X X 0 X^2+X 0 X^2+X X X^2+X X^2+X X^2+X X^2+X 0 X^2 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 0 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 0 0 0 0 X^2 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0 X^2 0 0 0 X^2 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 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 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 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+51x^68+84x^69+81x^70+112x^71+137x^72+152x^73+187x^74+166x^75+173x^76+226x^77+153x^78+114x^79+104x^80+78x^81+57x^82+42x^83+34x^84+26x^85+26x^86+14x^87+10x^88+10x^89+7x^90+2x^92+1x^122 The gray image is a linear code over GF(2) with n=304, k=11 and d=136. This code was found by Heurico 1.16 in 0.657 seconds.