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 1 1 1 1 1 1 1 1 1 1 X X X X X X X X X X X X X X^2 1 X^2 1 1 1 X 1 1 1 X 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 0 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 0 0 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 0 X^2 0 0 0 0 0 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 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 0 0 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 0 0 X^2 0 X^2 0 X^2 0 X^2 0 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 0 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 0 0 0 X^2 0 0 X^2 0 X^2 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 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 X^2 0 0 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 X^2 0 0 0 0 X^2 X^2 0 0 X^2 0 0 0 X^2 0 0 X^2 0 0 0 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 0 0 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 0 0 X^2 0 0 0 X^2 generates a code of length 89 over Z2[X]/(X^3) who´s minimum homogenous weight is 72. Homogenous weight enumerator: w(x)=1x^0+147x^72+415x^76+18x^78+618x^80+208x^82+920x^84+594x^86+2048x^87+1321x^88+4096x^89+752x^90+2048x^91+1222x^92+406x^94+709x^96+64x^98+416x^100+6x^102+251x^104+99x^108+23x^112+1x^120+1x^144 The gray image is a linear code over GF(2) with n=356, k=14 and d=144. This code was found by Heurico 1.16 in 41.5 seconds.