The generator matrix 1 0 0 1 1 1 0 1 1 X^2 1 X 1 0 1 X^2+X 1 X^2+X 1 1 X^2+X 1 1 X^2 X 1 1 X^2+X 1 X^2+X X 1 1 1 X^2 1 X^2+X 0 1 1 0 1 X 1 X^2+X 0 1 1 1 1 X^2+X X X^2+X X^2 0 X^2 1 1 0 X 1 1 X^2+X 1 1 1 1 0 X 1 1 1 X^2 X 1 0 X^2 1 X^2+X 0 1 0 1 0 0 1 1 1 X^2 1 1 X^2+1 1 X^2+X X^2+X X+1 1 X X X+1 X^2+X X^2 X 0 1 1 X+1 X+1 1 X^2+X 1 X 0 1 X 1 X^2+X+1 X^2 X^2 X 0 1 X+1 1 X^2+X+1 1 X X^2+1 0 X^2+X X 1 1 X^2 X^2+X X^2 1 0 1 1 X^2 X^2+1 X^2 0 1 X^2+X+1 X+1 1 1 1 X+1 X+1 X^2+1 0 X X 1 1 1 X 0 0 0 0 1 X+1 X^2+X+1 0 X+1 X 1 X^2+1 X X^2+X X+1 1 X 0 X 1 X^2+1 X^2+1 1 X^2 X^2+1 X 1 X^2 X^2+X+1 X^2+X+1 X^2+1 0 1 X^2+X X^2+1 X+1 X^2+X X^2+X 1 1 X X^2 X+1 X^2+X+1 1 X X 1 X+1 X+1 X X^2+X X+1 X^2+X 1 1 1 1 0 X^2+X+1 X+1 1 X^2+X X^2+X 1 0 X^2+1 X+1 X^2+X+1 X^2+X X^2+1 0 X^2+X+1 X^2 1 1 X+1 X^2 X^2 0 1 1 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 0 0 0 0 0 0 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 0 X^2 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 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+49x^74+152x^75+435x^76+364x^77+381x^78+334x^79+428x^80+274x^81+319x^82+242x^83+275x^84+202x^85+173x^86+120x^87+107x^88+40x^89+80x^90+42x^91+29x^92+14x^93+22x^94+6x^95+3x^96+2x^97+1x^100+1x^104 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 1.15 seconds.