The generator matrix 1 0 1 1 1 X^2 1 1 0 0 1 1 1 X^2 1 1 1 X^2 1 1 0 1 X^2 1 1 1 X^2+X 1 X^2+X 1 1 1 X 1 X^2 X^2+X 1 1 X 1 0 1 1 1 X^2 1 1 1 1 1 1 1 1 1 1 1 X 1 1 X^2 1 X^2+X 1 1 0 X^2+X 1 X 1 1 1 1 X X^2+X 0 1 1 1 X^2+X 1 X^2 0 1 1 0 1 1 X^2 X+1 1 1 0 X+1 1 1 0 0 X^2+1 1 X^2+1 0 1 X^2 1 X+1 X^2+X+1 X^2 1 X^2+X+1 1 X^2+X X+1 X 1 X^2+1 1 1 X^2+X+1 X^2+1 1 X 1 X 1 0 1 1 X^2+1 1 X^2 X X X^2+1 X+1 0 X+1 X+1 1 X 0 1 X 1 X^2 X^2+X+1 X 1 X^2+X 1 X X^2+1 1 0 1 1 1 X+1 0 X^2+1 1 1 1 0 0 X 0 0 0 0 0 0 0 0 X^2 X^2 X X X X^2+X X^2+X X^2+X X^2+X X^2+X X^2+X X X X^2 X^2 X^2+X X^2+X X^2 X X^2 X X X^2 0 X^2+X X^2+X X X 0 X^2 0 X X^2+X 0 X^2 0 X^2+X X^2+X 0 0 X^2 X^2 X^2 X^2 X 0 X 0 X^2 X 0 X^2+X X^2 X^2+X X^2+X 0 0 X^2 X^2+X 0 X X^2+X X^2 0 X X X^2+X 0 X X^2 0 0 0 X 0 0 X^2 X^2 X^2+X X^2+X X^2+X X X X X^2 X X X^2 0 0 0 X^2+X X^2+X X^2+X X^2 X^2+X X^2+X X^2 0 X^2 X^2+X X^2 X^2+X 0 0 0 X^2+X 0 X^2 X 0 0 X^2+X X X X X^2 X^2+X X X^2+X X X^2 0 X^2+X X^2+X X X 0 X^2 X^2 X X^2 X^2 X 0 X^2 X^2 X^2+X X^2+X X X^2+X X X^2+X X X 0 X^2+X X X^2+X X^2 X 0 0 0 0 X X^2+X X^2+X 0 X X^2 X X^2+X X^2 X X X^2 X X^2+X X 0 X^2 X 0 0 X^2+X X^2+X X^2 0 X^2+X X^2+X 0 X^2 X^2+X 0 X^2 X^2+X X^2 X^2 X^2 0 X X^2 X^2+X 0 X^2+X X^2+X X^2+X 0 X^2+X X^2+X X^2+X X 0 0 X^2+X X X^2 X X X^2 X^2+X X 0 0 X X 0 X^2 0 X^2 0 X^2+X X X^2+X 0 X^2 0 X^2+X X X X^2+X generates a code of length 81 over Z2[X]/(X^3) who´s minimum homogenous weight is 74. Homogenous weight enumerator: w(x)=1x^0+192x^74+140x^75+393x^76+228x^77+364x^78+228x^79+418x^80+336x^81+362x^82+276x^83+345x^84+196x^85+258x^86+92x^87+108x^88+40x^89+46x^90+24x^92+18x^94+12x^96+8x^98+8x^100+1x^104+2x^108 The gray image is a linear code over GF(2) with n=324, k=12 and d=148. This code was found by Heurico 1.16 in 2.99 seconds.