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 1 1 1 1 1 1 1 1 X^2 1 1 1 1 1 X 1 1 1 1 1 1 1 X^2 1 X 1 X 1 1 X 1 1 1 X^2 1 X 1 1 0 X 0 X 1 X^2 0 X 0 0 0 X X^2+X X X^2 0 X^2+X X^2+X X^2 X^2 X^2+X X^2+X X^2 0 X^2+X X^2+X 0 X X^2 X^2+X 0 X^2+X 0 0 X^2 X X X^2+X 0 X^2 X X^2 0 X X^2+X X^2+X X^2+X X^2 0 X^2 X 0 0 X 0 X^2 X X^2+X 0 0 X^2+X X^2+X X X 0 X^2 X^2 0 0 X^2+X X^2+X X X X 0 X X X^2 X^2 X X^2 0 X^2 X^2+X 0 0 0 X 0 X X X 0 X^2 0 X^2+X X^2 X X^2+X X^2+X X^2 0 X^2+X X 0 0 X^2 X^2+X X 0 X X X^2 X^2+X X X^2 0 0 0 X X X X^2 0 X^2+X 0 X^2 X^2 X X^2+X X^2+X X^2+X 0 0 X X^2 X^2 X 0 0 X^2 X^2+X 0 X^2+X X X X^2 X X^2 0 X X X^2 X X^2 0 0 X X^2+X X^2+X X X^2+X X^2+X 0 0 0 0 X X 0 X X^2+X 0 X^2+X X X^2 0 X 0 X^2+X X X^2 X^2+X X^2 0 X^2+X X^2+X X^2 0 X^2 X^2 X^2+X X^2+X X^2+X X^2+X 0 X^2 X X^2 0 X^2+X X^2+X 0 X^2+X 0 X 0 X X^2 0 X^2+X 0 X^2 X^2 0 X 0 X X X^2 X X X 0 X^2 X X^2+X X X^2 X^2 0 0 X^2+X 0 X^2 X^2+X X^2+X X^2 X^2+X 0 X X^2+X 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 0 0 0 0 0 X^2 0 X^2 0 X^2 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 X^2 0 X^2 0 0 X^2 0 0 X^2 0 0 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 X^2 X^2 generates a code of length 79 over Z2[X]/(X^3) who´s minimum homogenous weight is 72. Homogenous weight enumerator: w(x)=1x^0+183x^72+24x^73+82x^74+104x^75+210x^76+240x^77+62x^78+304x^79+167x^80+216x^81+40x^82+104x^83+113x^84+32x^85+48x^86+69x^88+22x^90+20x^92+2x^94+4x^96+1x^132 The gray image is a linear code over GF(2) with n=316, k=11 and d=144. This code was found by Heurico 1.16 in 0.747 seconds.