The generator matrix 1 0 0 0 1 1 1 1 X^2 1 X^2+X X 1 X^2 1 1 X 1 1 0 1 0 1 0 1 X^2 0 X^2 1 1 1 1 1 X X X^2+X 0 1 1 X^2+X 1 X^2+X X^2 1 X^2+X 0 1 1 1 1 1 1 1 X 1 1 1 1 1 X^2 1 0 1 1 1 1 X 0 1 0 X 0 X^2+X 1 1 X X X 0 X^2+X 1 0 1 0 0 0 X^2 1 X^2+1 1 X^2+X+1 X^2 1 0 1 X+1 X^2+1 1 X^2+X X^2+X+1 X X^2+1 1 X+1 1 0 X^2+X 1 1 X X^2+1 X^2+X 0 0 X^2+X 1 X^2 1 0 X^2+1 1 X^2+1 1 X X+1 X 1 1 X^2 0 0 X^2+X+1 X X 1 X^2+1 0 X^2+X X^2 X X^2+X X+1 1 X+1 X^2+X X^2+1 1 1 0 1 X^2+X 0 X 1 X X^2+1 X^2 1 1 1 X^2 X^2 0 0 1 0 0 X^2+1 1 X^2+X X+1 X^2+1 1 X^2 X^2+X+1 X^2+1 X^2 0 X^2 X^2+1 X+1 1 X^2+1 X^2+1 X^2 X^2+X X^2+X 1 X^2+1 X+1 0 X^2 1 1 X^2 X^2 X 1 0 1 X X^2+X+1 X+1 X 1 X 1 X+1 X^2+X+1 0 X^2+X X X X^2 X^2+X+1 X+1 X^2 X^2+X+1 1 1 X^2+1 X^2 X+1 X^2 X^2+X+1 X+1 X^2+X X+1 X^2 1 X^2+1 X^2+X X 1 X^2+X 1 X^2+1 X^2 X^2 X^2+X X^2+X+1 X^2 X 0 0 0 1 1 1 X^2 X+1 X+1 X^2+1 X^2+1 X^2+1 X X X^2 X^2+X+1 0 X^2+1 X^2+X+1 X^2+1 X^2 X^2 X 1 X^2+1 0 X^2+X+1 0 X^2+X X X+1 X^2 X^2+X 1 X^2 X^2+1 1 X^2+X X^2+1 X^2 1 X X X^2 X^2+1 X^2 0 X^2+1 X^2+1 X^2+X 1 1 X+1 X+1 X X^2+X+1 X^2 X+1 X 1 0 X+1 X^2+X+1 X^2+1 X+1 X+1 X^2+X X^2+X+1 X+1 1 1 X^2+X+1 X^2+X+1 X^2+X+1 X 1 X+1 X^2+X X^2+X+1 1 X^2+X 0 0 0 0 X 0 0 0 0 X X X X^2+X X X X^2 X^2 0 0 X^2 X X^2 0 X^2+X 0 X^2+X X X^2 X X^2+X X^2+X X^2 X^2 X^2+X X X^2 X^2 0 X X^2 0 X^2+X 0 X^2 0 X X^2+X 0 X^2+X X^2+X X^2+X X^2 X^2 X^2 0 X X X X X X^2 X^2 X^2+X X X^2 X^2+X X^2+X X^2 X^2+X X 0 X^2 X^2+X 0 X^2+X X X X^2 X^2+X 0 X^2 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+98x^72+362x^73+719x^74+794x^75+862x^76+1148x^77+1101x^78+1254x^79+1473x^80+1278x^81+1236x^82+1296x^83+1060x^84+916x^85+849x^86+606x^87+508x^88+338x^89+200x^90+140x^91+48x^92+48x^93+18x^94+4x^95+12x^96+6x^97+5x^98+2x^99+2x^100 The gray image is a linear code over GF(2) with n=324, k=14 and d=144. This code was found by Heurico 1.13 in 5.03 seconds.