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 1 1 1 1 1 1 X^2 1 1 1 1 1 1 1 1 0 1 1 1 1 X^2 1 X^2 1 1 1 0 X 0 X^2+X 0 X^2+X 0 X^2+X X^2 X^2+X 0 X^2+X X 0 X^2 X X^2 X^2+X X^2+X 0 0 X^2+X X X^2 X^2+X 0 X 0 0 X^2+X X^2+X X^2 0 X X 0 X^2 0 X^2+X X X^2+X X^2 X^2+X X^2+X X^2 X^2 0 X 0 X X^2 X^2 X^2+X 0 X^2+X X^2 X^2+X 0 X^2 X X^2 X 0 0 X^2+X X^2 X^2+X X^2 0 0 0 0 0 X^2 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 0 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 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 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 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 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 X^2 X^2 0 0 0 0 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 0 X^2 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 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 0 X^2 X^2 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 0 X^2 0 0 0 X^2 0 0 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 0 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 0 X^2 0 0 X^2 0 0 0 0 generates a code of length 71 over Z2[X]/(X^3) who�s minimum homogenous weight is 64. Homogenous weight enumerator: w(x)=1x^0+79x^64+152x^67+16x^68+256x^69+71x^70+32x^71+8x^72+256x^73+16x^74+16x^75+16x^76+8x^78+32x^79+8x^80+16x^82+24x^83+16x^86+1x^134 The gray image is a linear code over GF(2) with n=284, k=10 and d=128. This code was found by Heurico 1.16 in 0.312 seconds.