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 1 1 1 1 1 1 1 1 1 1 1 1 X^2 1 1 1 1 1 1 1 X 1 1 0 1 1 1 1 1 1 1 1 X X X 1 0 X 0 X^2+X 0 X^2+X 0 X^2+X X^2 X^2+X X^2+X 0 X^2+X 0 X^2 X 0 X^2+X X X^2 0 X^2+X X^2 X 0 X^2+X X X^2 X^2+X 0 0 X^2+X X^2 X X^2 X X^2+X 0 X^2+X 0 X X^2 0 X X^2+X X^2 0 X^2+X 0 X^2+X X^2 X 0 X^2+X X^2 X^2 X^2+X X^2+X X 0 0 0 X^2 0 X^2+X X X^2 X^2 X^2 X^2+X X 0 X^2 X^2+X X X^2+X X^2+X 0 0 0 0 X^2 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 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 0 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 0 X^2 0 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 0 0 0 0 0 X^2 0 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 0 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+22x^72+16x^73+46x^74+58x^75+42x^76+130x^77+34x^78+424x^79+25x^80+86x^81+25x^82+8x^83+20x^84+14x^85+14x^86+16x^87+16x^88+10x^89+8x^90+6x^91+2x^92+1x^146 The gray image is a linear code over GF(2) with n=316, k=10 and d=144. This code was found by Heurico 1.16 in 0.435 seconds.