The generator matrix 1 0 1 1 1 X^2+X 1 1 X^2 1 1 X 1 1 X 0 1 1 1 X^2 X^2+X 1 1 1 1 1 1 X 1 1 1 1 1 1 1 1 X^2+X 1 1 1 1 1 1 1 1 1 1 0 1 1 X X^2+X 1 1 X^2 1 0 1 1 1 X 1 1 1 X X X 1 0 X 1 1 X 1 1 1 X^2 1 X^2 1 X^2+X 0 1 1 0 X^2+X+1 1 X+1 X^2+X 1 X^2 X^2+1 1 X X^2+X+1 1 1 X^2+X+1 X^2+X X^2+1 1 1 X^2+X X^2+1 X 0 X+1 X 1 1 X^2+X 1 X^2+X X^2+X 1 X X^2+X+1 1 X^2 X^2+X+1 0 X^2 1 X+1 X^2+X+1 0 X X+1 1 0 0 1 1 X^2+1 X+1 1 1 1 1 0 1 1 X^2+X X 1 1 1 1 X^2+1 1 1 1 X^2+1 X^2 X+1 X^2 X^2+X+1 1 X^2+X+1 X 1 1 0 0 X 0 X^2+X 0 X^2 X^2 X X^2+X 0 X^2+X X^2+X X^2 0 X^2+X X^2+X X^2+X X^2 X^2 X^2+X X^2+X X^2+X X^2 X 0 0 X 0 X^2+X X X^2+X X^2 X^2 X^2+X X^2+X 0 X^2+X 0 X X 0 0 X^2+X X^2 X^2 X X^2 X^2 X^2 X^2 X X^2+X X^2+X X^2+X 0 X^2+X X^2+X 0 0 0 0 X^2 X X 0 X^2 0 X^2+X X^2 X X^2 0 X^2 X^2 X 0 X X 0 X 0 0 0 X 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2+X X^2+X X X X^2+X X X^2+X X^2+X X^2+X X^2+X X^2+X X^2+X X^2 0 X^2 X^2+X 0 X^2 X^2+X X^2+X X^2 X^2 X X^2+X 0 X X^2 X^2 X^2+X X^2+X X^2 0 X^2+X X^2+X X^2 X^2+X X^2 X^2+X X^2 X X^2 X^2+X X^2 X^2 X^2+X X^2 X X^2 X X 0 X X X^2 X 0 X X X X 0 X^2 X 0 X^2 X^2 X^2+X 0 0 0 0 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 0 X^2 0 0 X^2 X^2 0 0 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 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+181x^74+116x^75+442x^76+252x^77+400x^78+252x^79+324x^80+300x^81+353x^82+284x^83+335x^84+196x^85+290x^86+116x^87+99x^88+20x^89+59x^90+28x^92+18x^94+15x^96+11x^98+2x^100+1x^108+1x^112 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 1.54 seconds.