The generator matrix 1 0 0 0 0 0 1 1 1 0 1 X 1 0 X X 1 X 1 1 1 X X 1 X X 1 1 0 0 1 X 0 0 0 1 X 1 1 0 1 1 1 X 1 1 X 0 0 1 X 0 1 X 1 1 1 X 1 0 1 1 1 0 X 1 X X X 1 1 1 X 0 0 0 X X 1 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 X X X X 0 X X X 0 1 1 1 X+1 1 1 1 1 X+1 1 X+1 1 1 1 X+1 X+1 1 X+1 1 1 1 1 1 X 1 1 1 1 0 X X X+1 0 X 1 1 X 0 X+1 X X 1 0 0 X+1 X X 1 0 1 1 1 1 X+1 X 0 0 0 1 0 0 0 0 0 X X 1 1 X+1 1 X 1 X 1 X 1 X+1 1 0 X 0 1 1 0 X+1 X 1 X+1 0 X+1 1 0 X 1 1 X 1 X+1 X X 0 X 0 X X X 0 1 1 X X 1 1 X 0 0 1 X+1 1 1 1 X+1 X 1 0 0 0 1 1 X 1 X X X+1 0 X X X 0 0 0 0 1 0 0 X 1 X+1 1 0 1 1 X+1 1 X+1 1 0 0 X+1 X+1 0 1 X X X+1 0 X+1 1 0 X 1 X+1 X 0 1 X X+1 1 X+1 1 1 X 0 1 X 0 1 1 X+1 X X+1 0 0 1 1 1 1 X X 0 0 0 X+1 0 X X 1 X+1 1 X 0 X 1 0 1 X+1 1 X X+1 X X 0 0 0 0 0 1 0 X+1 1 0 1 X X+1 X+1 1 X 0 0 X+1 1 X+1 0 X X+1 0 1 X X+1 1 X 0 0 1 X X+1 1 X 1 1 X+1 X X 0 X+1 X+1 0 X+1 0 X+1 1 1 1 X+1 X+1 1 X X+1 X X+1 0 1 1 0 1 0 1 1 1 X+1 X 0 1 0 0 0 X 1 1 0 X+1 1 X 0 X 0 0 0 0 0 1 1 X 1 1 X+1 X 1 X+1 X+1 X 0 0 X X X+1 1 0 1 1 X+1 X 1 X X+1 X+1 X+1 X 0 1 0 1 1 X X+1 1 0 X X X+1 X+1 X+1 1 X X X+1 0 X+1 X+1 0 0 X X 1 1 X+1 X X 0 X 0 0 X+1 1 1 0 X X X+1 X 0 1 0 1 0 1 X+1 X 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+59x^72+106x^73+111x^74+198x^75+252x^76+190x^77+222x^78+230x^79+229x^80+254x^81+211x^82+240x^83+213x^84+206x^85+200x^86+158x^87+158x^88+138x^89+131x^90+132x^91+85x^92+90x^93+90x^94+60x^95+49x^96+38x^97+23x^98+6x^99+10x^100+2x^101+4x^102 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 3.02 seconds.