The generator matrix 1 0 1 1 1 X^2+X 1 1 X^2 1 X 1 1 X^2 1 X^2 1 1 X^2+X 1 1 1 1 X^2+X 1 1 1 0 X^2 1 1 1 1 X 0 1 1 X X^2 X 1 1 1 1 1 0 1 1 X^2+X X 1 1 1 1 1 1 1 1 0 1 1 0 X^2 1 X 1 1 1 0 1 1 1 1 X 0 1 X 0 1 1 1 0 1 1 0 1 1 X X^2+X+1 1 1 1 X^2+X X+1 1 X^2 1 1 X^2+X 1 0 X+1 X^2+X X+1 1 X^2+1 X 0 1 1 1 X X^2+1 0 1 1 X^2+1 X 1 1 1 X^2+X+1 X^2+X X X^2+1 0 1 1 X^2+X+1 1 1 X^2+X+1 X^2 X^2+1 X^2 1 X^2 1 1 1 X^2+X X^2+X 1 1 1 1 X X^2 X+1 1 1 X+1 X+1 0 X^2+X 1 X^2+1 1 X X X^2+X X^2 0 0 X 0 0 0 0 0 0 X^2 X^2 0 0 X X^2+X X^2+X X X X X X^2+X X X X 0 X^2+X X^2 0 X^2+X X 0 0 X^2+X X^2 X X^2 0 X X^2 X^2+X 0 X^2+X X^2+X X^2 X^2 X^2+X X X X^2+X X^2 X^2 X^2+X X^2+X 0 X 0 0 X^2 X^2 X^2+X X X^2+X X^2+X 0 X^2 X^2 X^2+X X^2 X^2 X^2 X 0 X 0 X^2 0 X^2 X^2+X 0 X^2 0 0 0 0 X 0 0 X X X X^2+X X X^2 0 X^2 0 X X X X^2 X 0 0 X^2+X X^2+X 0 X X^2+X X^2+X X^2 X X^2 X^2+X 0 X^2 0 0 X X^2+X X^2 X^2+X X^2+X 0 X X X X X^2+X X^2 X^2 X 0 0 0 X^2 X^2 X^2 X^2+X X 0 X^2 X^2+X X^2 X X X^2+X 0 0 X X^2+X X^2 X^2+X X^2+X X^2 X X^2 X^2+X X^2+X X^2 X^2+X X^2+X X^2 0 0 0 0 X 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X X X X^2+X X X^2+X X^2+X X^2+X X X X^2+X X X^2+X X^2+X X^2+X X X^2+X X^2+X X X^2 X^2+X X X^2 X X^2+X X 0 X X^2+X X^2+X X^2+X X^2 X X^2 X^2 X^2 X 0 X X X^2 X X X X^2 X^2 X^2 X X X^2 0 X^2 X X^2 0 X^2+X 0 0 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 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 0 X^2 0 X^2 X^2 0 0 0 0 X^2 0 0 0 X^2 X^2 0 0 0 0 0 0 0 0 0 0 X^2 X^2 0 0 X^2 X^2 0 generates a code of length 81 over Z2[X]/(X^3) who´s minimum homogenous weight is 72. Homogenous weight enumerator: w(x)=1x^0+116x^72+64x^73+436x^74+256x^75+583x^76+392x^77+734x^78+528x^79+832x^80+636x^81+768x^82+468x^83+609x^84+384x^85+494x^86+280x^87+283x^88+60x^89+96x^90+4x^91+69x^92+56x^94+22x^96+8x^98+10x^100+2x^104+1x^108 The gray image is a linear code over GF(2) with n=324, k=13 and d=144. This code was found by Heurico 1.16 in 6.23 seconds.