The generator matrix 1 0 0 0 1 1 1 0 1 1 1 X 0 X 1 1 1 1 X 1 0 0 1 0 1 X 1 1 0 0 0 X 0 0 1 0 0 0 X 1 1 X X 1 1 1 1 0 0 X 1 X 1 X 1 1 X 1 1 1 1 1 1 1 1 X X 1 0 1 1 1 1 1 0 1 1 X 1 X 1 1 1 0 1 0 0 0 1 1 1 X 0 X+1 1 1 X X+1 X+1 0 0 1 0 1 1 X+1 1 1 1 X+1 0 X 0 X 1 0 1 X+1 1 X 0 1 1 0 1 X 1 1 1 X X 0 1 X 0 1 1 1 X X X+1 1 X X 1 1 X X 0 1 1 0 X+1 1 X+1 X X 0 1 X+1 1 0 1 0 X X+1 0 0 1 0 1 1 0 1 0 X+1 X 0 X+1 1 1 X X+1 X X 1 X+1 X X+1 1 0 X+1 1 X 0 1 1 X 1 X+1 1 1 X 1 X X 0 X+1 X X 1 X+1 X+1 1 0 X 1 1 X+1 0 0 1 1 0 X+1 1 X+1 0 1 1 1 1 0 X+1 1 X 0 1 X 1 X 0 0 0 X 1 X 0 1 0 0 0 1 1 0 1 1 1 0 X X+1 X X+1 X+1 0 0 X X+1 X+1 X+1 0 X X X+1 X+1 X X+1 1 0 0 X 1 X X+1 0 1 X 0 1 0 1 1 1 X+1 0 X X+1 1 1 X X X+1 X+1 X+1 1 0 1 0 0 X X X+1 X X X+1 X 0 0 0 1 0 1 1 1 X+1 0 X X+1 0 X 1 1 0 0 0 0 X 0 0 0 0 X 0 X X X 0 X 0 X 0 X 0 0 0 X 0 0 X X 0 0 X 0 0 X 0 X 0 X X X 0 0 0 X 0 X 0 0 0 0 X X X X 0 0 0 X X 0 0 0 X 0 X 0 X X 0 X X 0 0 X X X 0 X X X 0 X X 0 0 0 0 0 X 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 X X X X X X X 0 0 0 0 X 0 X X X X 0 0 X X X X 0 X 0 X 0 X 0 X X X X X X X 0 0 X X 0 X X X 0 0 X X 0 X X 0 X 0 0 0 X 0 0 X 0 0 0 0 0 0 0 X 0 0 0 X 0 0 0 X 0 X 0 X X X 0 X 0 X X X 0 X X 0 0 0 X 0 X X 0 0 X X X X 0 X X X X 0 0 0 0 0 X X X 0 0 0 0 X 0 0 0 X X X X X 0 X X 0 0 0 0 0 0 X 0 0 0 X 0 0 0 0 0 0 0 X 0 0 0 X 0 X X X X X 0 0 X X 0 X X 0 X 0 0 0 X X X X X 0 0 0 0 0 0 X X X 0 0 0 X X 0 X X 0 X 0 0 X 0 X 0 X 0 X 0 0 0 X 0 X X 0 X X X X 0 X X X X X X 0 generates a code of length 83 over Z2[X]/(X^2) who´s minimum homogenous weight is 72. Homogenous weight enumerator: w(x)=1x^0+56x^72+78x^73+146x^74+186x^75+230x^76+228x^77+201x^78+270x^79+216x^80+246x^81+255x^82+194x^83+207x^84+204x^85+157x^86+174x^87+175x^88+168x^89+155x^90+118x^91+90x^92+80x^93+73x^94+66x^95+39x^96+18x^97+27x^98+14x^99+9x^100+9x^102+2x^103+1x^104+2x^105+1x^106 The gray image is a linear code over GF(2) with n=166, k=12 and d=72. This code was found by Heurico 1.16 in 3.25 seconds.