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 0 1 1 1 1 1 X^2 1 X^2 1 0 X 0 X^2+X 0 X^2+X 0 X 0 X^2+X X 0 X^2+X 0 X^2 X^2+X 0 X^2+X X^2 X^2+X X^2 X^2+X X^2 X X^2+X 0 X X^2 0 X^2+X 0 X^2+X X^2 X X^2 X 0 X^2+X X^2+X 0 X^2 X^2+X 0 X X X^2 0 X 0 X^2 X X^2 X 0 0 X^2+X X^2+X X^2+X X X^2 0 X^2 0 X^2 X^2+X X^2 X X^2 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 0 0 X^2 0 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 X^2 0 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 0 X^2 X^2 0 0 X^2 0 0 0 0 0 X^2 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 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 0 0 X^2 X^2 0 X^2 0 X^2 0 0 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 0 0 0 0 0 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 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 0 0 0 0 generates a code of length 69 over Z2[X]/(X^3) who´s minimum homogenous weight is 64. Homogenous weight enumerator: w(x)=1x^0+79x^64+152x^65+71x^66+256x^67+16x^68+32x^69+16x^70+256x^71+8x^72+16x^73+8x^74+16x^76+32x^77+16x^78+8x^80+24x^81+16x^82+1x^130 The gray image is a linear code over GF(2) with n=276, k=10 and d=128. This code was found by Heurico 1.16 in 0.29 seconds.