The generator matrix 1 0 0 0 0 0 1 1 1 X 0 0 0 0 1 1 1 1 0 X 1 1 X 0 1 1 1 X 1 0 0 1 0 X X 1 1 0 1 X 1 1 1 0 1 X 1 0 1 X 0 X X 0 1 1 1 1 1 1 1 1 1 0 1 0 1 X 0 1 1 1 1 1 X X 0 X 1 X X 0 1 0 0 0 0 0 0 0 0 1 X 1 1 0 X 1 1 1 1 X 1 X 1 0 X+1 1 X X+1 1 1 0 X X 0 X+1 0 X 1 0 1 1 X 0 X+1 1 X 1 X 1 1 0 X 1 X+1 X 0 1 1 0 1 1 X X 1 0 1 1 1 X 0 X+1 X+1 X 1 0 X 1 X+1 1 1 0 0 1 0 0 0 0 0 0 0 X 1 1 X+1 X+1 X+1 X 0 1 X+1 0 X+1 1 0 X+1 X 0 1 X+1 X 0 X+1 1 1 1 1 X+1 X X X 0 1 X+1 X 0 1 0 X+1 X 0 1 0 0 X 1 X+1 1 0 1 X+1 X+1 1 0 X X+1 1 0 X X X+1 1 X X X 1 1 0 1 X X+1 X 0 0 0 1 0 0 0 1 1 1 X+1 X+1 1 X 0 X+1 0 X+1 X X+1 X+1 0 X X X X 1 X+1 1 X+1 X+1 X 0 0 1 1 1 1 X+1 1 X X X 1 0 0 X+1 0 0 0 0 1 1 1 X X X+1 0 X X+1 1 1 0 0 0 0 0 X X 0 1 1 0 1 1 1 1 X X+1 0 1 0 0 0 0 1 0 1 1 X X+1 1 1 1 0 X+1 0 1 X X+1 0 1 0 X+1 1 X 0 X+1 X 0 X+1 0 1 X+1 0 1 X+1 X+1 X X 1 X+1 X X+1 X+1 0 X 1 X+1 X X 1 0 X+1 X 1 X+1 1 1 X+1 1 0 0 X 1 X 0 X+1 0 1 X 0 1 1 X 0 X 0 X+1 1 X+1 1 0 0 0 0 0 1 1 X X+1 1 0 X 1 X+1 0 X X X X 0 0 0 1 X+1 1 X+1 X+1 X+1 X+1 0 X+1 0 1 X X X 1 X X 1 0 X+1 X+1 X X X X+1 1 1 1 X+1 X+1 X X+1 1 X+1 X 1 1 0 0 1 1 1 X X+1 0 X+1 1 X+1 0 X+1 0 X+1 1 0 X+1 0 X 1 X 0 0 0 0 0 0 X 0 X 0 0 0 0 0 X X X X 0 0 X X 0 0 X 0 0 X 0 X X 0 X X X 0 0 X 0 X 0 0 0 X X 0 0 X X X 0 X 0 0 0 X 0 0 X X 0 X X X 0 0 0 X X 0 X X 0 0 X X 0 0 0 X 0 generates a code of length 81 over Z2[X]/(X^2) who�s minimum homogenous weight is 69. Homogenous weight enumerator: w(x)=1x^0+86x^69+166x^70+228x^71+265x^72+330x^73+379x^74+382x^75+402x^76+390x^77+442x^78+448x^79+456x^80+440x^81+451x^82+426x^83+388x^84+416x^85+362x^86+340x^87+313x^88+254x^89+221x^90+178x^91+128x^92+114x^93+83x^94+40x^95+27x^96+16x^97+5x^98+6x^99+2x^100+2x^101+2x^102+2x^104+1x^110 The gray image is a linear code over GF(2) with n=162, k=13 and d=69. This code was found by Heurico 1.16 in 13.4 seconds.