The generator matrix 1 0 0 1 1 1 X 1 X^2+X 1 1 X 1 X^2+X 1 X X^2 1 1 X 1 1 0 0 1 1 1 X 0 X^2 1 1 X 1 1 1 1 0 X^2+X 1 X^2 1 1 X 0 1 X X^2+X 1 1 1 X^2+X 1 1 1 X^2 1 0 0 X^2 X^2 1 1 1 X X^2+X 1 X^2+X X 1 X 1 0 1 0 0 1 X^2+X+1 1 X^2 0 X^2 X^2+X+1 1 X+1 1 1 X^2+X 1 X X 1 X X^2+1 X 1 X+1 1 X^2 1 1 X^2 1 1 1 X^2+X X^2 X^2 X^2+X+1 1 X 0 1 X+1 1 X^2 1 1 1 1 0 0 X+1 1 X^2+X+1 X X^2+X+1 X^2+X 0 1 1 0 X^2+X X^2+1 1 X 1 X^2+X X 1 1 X^2+1 X^2+X X^2+X 0 0 1 1 X+1 0 1 X+1 1 X X+1 X X X+1 X^2+1 1 X X^2+X 0 X^2 X+1 X^2+X 1 X+1 0 1 1 1 X^2+X 1 0 X^2+X+1 X+1 1 X^2+X+1 X^2 0 X^2+X+1 1 X^2+1 X X^2+X 1 1 X^2+X+1 X X^2+X+1 X 1 X^2+1 1 X+1 X^2+X X+1 X^2+X 1 X 0 X^2 1 1 X+1 0 X+1 1 1 1 1 0 X^2+1 1 X^2+X 0 0 0 X X X^2+X X^2 X^2+X 0 0 X X^2 X 0 X^2+X 0 0 X^2 X^2 X^2 X^2+X X 0 X^2 X^2+X 0 0 X^2+X X^2+X X^2+X X^2 0 X^2+X X^2 X^2+X X^2+X X^2 X X^2+X X^2 X^2+X X^2 X X 0 0 X^2+X X^2+X X^2+X X^2 0 0 X 0 X^2+X X^2+X X^2+X X^2+X 0 X 0 0 X X^2 X X^2+X X X^2+X X^2+X X^2 X^2+X X^2+X 0 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 0 0 0 0 0 0 0 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 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 generates a code of length 72 over Z2[X]/(X^3) who´s minimum homogenous weight is 64. Homogenous weight enumerator: w(x)=1x^0+68x^64+258x^65+398x^66+472x^67+649x^68+708x^69+687x^70+760x^71+639x^72+560x^73+636x^74+618x^75+535x^76+398x^77+277x^78+216x^79+130x^80+54x^81+49x^82+34x^83+18x^84+2x^85+12x^87+6x^88+4x^89+1x^90+2x^92 The gray image is a linear code over GF(2) with n=288, k=13 and d=128. This code was found by Heurico 1.16 in 3.54 seconds.