The generator matrix 1 0 1 1 1 X^2+X 1 1 0 1 X^2+X 1 1 1 0 1 1 X^2+X X^2 1 1 1 1 X 1 1 0 1 1 X^2+X 0 1 1 1 1 X^2+X 0 1 1 1 1 X^2+X 1 1 X^2 1 1 X X X X X 1 1 1 0 X^2 X^2+X X X X X^2+X X^2 X 0 1 1 X 1 1 1 1 1 1 1 X 0 0 1 X+1 X^2+X 1 1 0 X+1 1 X^2+X 1 X^2+1 X+1 0 1 X^2+X X^2+1 1 1 X^2 X^2+X+1 X X^2+1 1 0 X+1 1 X^2+X X^2+1 1 1 0 X+1 X^2+X X^2+1 1 1 0 X+1 X^2+1 X^2+X 1 X^2 X^2+X+1 1 X 1 1 0 X^2 X^2+X X X+1 X^2+X+1 1 X X 1 1 1 1 1 X 1 X X^2+1 X^2+X+1 X^2+X X^2+1 X^2+X+1 X+1 1 X^2+1 X^2+1 1 0 X 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 X^2 0 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 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 0 0 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 0 0 X^2 X^2 0 0 0 0 X^2 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 generates a code of length 77 over Z2[X]/(X^3) who´s minimum homogenous weight is 72. Homogenous weight enumerator: w(x)=1x^0+108x^72+56x^73+152x^74+64x^75+142x^76+52x^77+130x^78+36x^79+143x^80+16x^81+64x^82+24x^83+10x^84+4x^85+2x^86+4x^87+8x^88+4x^90+2x^92+1x^100+1x^132 The gray image is a linear code over GF(2) with n=308, k=10 and d=144. This code was found by Heurico 1.16 in 0.289 seconds.