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 1 1 1 1 1 1 X^2 1 1 1 1 1 X 1 1 1 1 1 1 X X X X X X 0 X 0 X^2+X 0 X^2+X 0 X^2+X X^2 X^2+X X^2+X 0 0 X^2+X X X^2 0 X^2+X X X^2 0 X^2+X X^2 X 0 X^2+X X^2+X 0 X X^2 X^2 X 0 X^2+X X^2+X 0 0 X^2+X X^2 X 0 X^2 X X^2+X X X^2 0 X 0 X^2 X X 0 X^2+X 0 X^2+X X X^2 X 0 X^2+X X^2+X X^2 X^2 0 X^2 0 X^2 0 X^2 X^2+X X^2+X X^2+X X^2+X X^2+X 0 0 0 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 0 0 0 0 0 X^2 0 0 0 X^2 0 0 0 0 0 X^2 X^2 0 0 X^2 0 0 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 0 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 0 0 X^2 0 0 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 X^2 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 X^2 X^2 0 0 X^2 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 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 0 0 0 0 X^2 0 X^2 0 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 0 0 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 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 0 0 X^2 0 0 0 X^2 X^2 0 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 generates a code of length 76 over Z2[X]/(X^3) who´s minimum homogenous weight is 69. Homogenous weight enumerator: w(x)=1x^0+24x^69+30x^70+52x^71+85x^72+30x^73+138x^74+8x^75+144x^76+274x^77+82x^78+36x^79+25x^80+34x^81+6x^82+16x^83+22x^85+16x^87+1x^136 The gray image is a linear code over GF(2) with n=304, k=10 and d=138. This code was found by Heurico 1.16 in 3.93 seconds.