The generator matrix 1 0 0 1 1 1 X^2+X 1 X 1 1 1 0 X 0 X 1 1 1 1 X^2+X 1 X^2+X X^2+X 1 1 1 0 1 1 0 X^2 1 0 1 1 1 X^2 1 X^2+X 1 X 1 1 0 1 1 0 1 X 1 X^2 X^2 1 X^2 1 X^2+X 1 1 0 1 1 1 X^2 1 X 1 0 1 1 1 1 1 1 X^2 1 1 1 1 X 1 0 1 0 0 1 X+1 1 X^2+X 0 X+1 X^2+X 1 1 1 X^2+X 1 1 X^2+1 X X^2+X 1 1 1 1 X^2+X 1 X^2+X X^2 X^2 X+1 1 1 X+1 X^2+X X^2+X X^2+X+1 X^2 1 X^2+X+1 X X^2+X+1 1 X^2+X X 1 X^2+1 X+1 1 X^2 1 0 1 1 X 0 X^2+X 1 X^2+X+1 X^2+1 X^2 X^2+X+1 X^2+1 X+1 X X+1 1 X X X^2+X X^2+X X+1 X^2+X+1 X^2 X+1 1 0 X^2+X X 1 1 X^2+X+1 0 0 1 1 1 0 1 1 1 X^2+1 0 X^2 1 X^2 1 X^2+X X^2+X X+1 X^2+X X^2+X+1 X+1 X X^2+X X^2+X+1 X X+1 X^2+1 1 X^2+X X X+1 X X^2+1 1 X^2+1 X^2+1 0 0 X+1 1 X^2 0 X^2+X+1 X^2+X+1 0 X^2+1 X^2 1 X X^2+1 X+1 0 1 0 1 X^2 X^2+1 X+1 X 1 1 0 X^2+X 1 0 1 0 1 X+1 X^2+X+1 X X^2 X X^2+X+1 X+1 X^2+1 1 X^2+1 X^2 X^2+X+1 X+1 0 0 0 X 0 0 X^2 X^2 X^2 X^2+X X X X^2+X X X 0 X^2 X^2+X 0 X^2+X X X X 0 X X^2 X^2 X^2+X X^2+X X^2+X 0 0 0 0 X X^2+X X^2 X^2+X X^2+X X X X^2+X 0 X 0 0 0 X^2 X^2 X^2+X 0 0 X X X^2 X^2 X^2 X^2+X 0 X^2 X^2 X X^2 0 X^2+X 0 X^2+X X^2+X X^2 0 X^2 X^2+X X X^2+X 0 X^2 X 0 X X^2 X^2 0 0 0 0 X X^2 X X^2+X X^2+X X^2 X X^2+X 0 X 0 X^2+X X X^2+X X X^2+X X^2+X X^2 0 0 0 0 0 X^2+X X X^2+X X^2+X X^2 X^2+X X^2 X^2+X X^2+X X X^2+X X^2 X^2 X^2 X^2 X^2 0 X X^2 X 0 0 X X X^2+X 0 X^2 X X^2 X^2+X X^2+X 0 X^2 X 0 X X^2+X 0 X^2 X^2 0 X^2 X^2+X 0 X X 0 0 X^2+X X^2 X^2 X^2 X X^2+X generates a code of length 81 over Z2[X]/(X^3) who´s minimum homogenous weight is 73. Homogenous weight enumerator: w(x)=1x^0+102x^73+232x^74+488x^75+540x^76+606x^77+735x^78+690x^79+656x^80+592x^81+657x^82+566x^83+511x^84+442x^85+390x^86+318x^87+221x^88+182x^89+85x^90+52x^91+50x^92+38x^93+9x^94+12x^95+4x^96+4x^97+4x^98+2x^99+1x^100+2x^101 The gray image is a linear code over GF(2) with n=324, k=13 and d=146. This code was found by Heurico 1.16 in 4.92 seconds.