The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 0 1 1 1 X X^2 1 1 1 1 0 1 1 1 1 X X 1 1 X^2 0 1 0 1 1 1 1 X^2 1 X 1 0 1 1 X 1 1 1 1 X 1 1 1 1 0 X 0 0 0 0 0 0 X^2 X X^2+X X^2+X X X X^2+X X^2+X X^2 X^2 0 X X X^2+X X 0 X X 0 X^2+X X X^2 X^2 X^2 X^2+X X^2+X 0 X^2+X X^2+X X X^2 X^2+X X^2+X X^2+X X X^2 X 0 X^2+X 0 X^2+X 0 X^2 X X 0 X X 0 0 X^2 0 X^2 X^2+X 0 X^2 X X^2+X X^2+X X^2 0 X X^2+X X^2+X X X^2+X X X^2+X X^2 0 0 0 X 0 0 X 0 0 0 X X^2+X X^2+X X X X^2 X X X^2 0 X^2 X^2+X X^2+X X^2+X 0 X X^2+X X^2+X 0 X^2+X X^2+X X^2 X^2 0 0 X^2 X^2 X^2+X 0 X^2+X X^2+X X^2+X X^2 X^2 X^2+X 0 X^2 X^2 X^2+X X X X^2 X^2 X X^2 X^2 X X^2+X X X X^2 X X^2+X X X X^2+X 0 X^2+X X^2 X X X^2+X X^2 0 X^2 X^2 X^2+X X X^2+X 0 0 0 0 X 0 0 0 0 X 0 X X X 0 X^2 0 X X^2+X X^2+X X X^2 X^2 0 0 0 X^2 X^2 X^2+X X X^2+X X X 0 X X^2 X^2+X X^2+X X^2+X X X^2+X X^2+X X^2+X X X 0 X^2 X^2 X^2 0 X^2+X X^2 X^2 X^2 X^2 X^2+X X^2+X X^2+X X^2+X 0 0 X X X X X 0 X X X X 0 X^2 X^2 0 0 0 0 X X X^2 0 X X^2+X 0 X X^2 0 0 0 0 X X X^2 X^2+X X X^2 X 0 X 0 X X X^2+X X^2+X 0 X^2 X X X^2 0 X^2 X^2+X X^2+X 0 X 0 X^2 X X^2+X X X^2+X X^2 X^2+X X^2 0 0 X X^2 X X^2 X^2 X^2 0 X 0 X X^2 X^2 X 0 X^2+X 0 X X^2 0 X^2+X X X X^2 X^2+X X^2+X X^2 X X^2 X X X 0 X^2 X X^2 X^2+X 0 X^2 X^2 X X^2+X 0 0 0 0 0 X^2 X^2 X^2 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 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+111x^72+254x^74+20x^75+376x^76+108x^77+378x^78+244x^79+535x^80+300x^81+458x^82+220x^83+326x^84+100x^85+218x^86+28x^87+175x^88+4x^89+120x^90+54x^92+36x^94+18x^96+8x^98+3x^100+1x^132 The gray image is a linear code over GF(2) with n=324, k=12 and d=144. This code was found by Heurico 1.16 in 1.9 seconds.