The generator matrix
1 0 0 0 0 1 1 1 0 1 1 X 1 0 1 0 0 1 X 1 1 X 0 X 1 X 1 1 X X 1 1 1 1 1 X 0 X 1 1 0 0 1 1 1 1 1 X 1 X X 1 X X 1 1 0 X 1 1 1 0 0 0 0 X 1 1 0 0 0 X 1 0 1 1 X 0 1 X 1
0 1 0 0 0 0 0 0 0 1 1 1 1 1 X+1 X 1 1 1 1 X 0 1 0 X 1 0 X+1 0 X 1 X+1 X 0 X 0 1 1 0 X+1 1 1 X+1 1 X X+1 X+1 X X 1 1 0 1 0 X+1 0 X 1 0 X X+1 0 X X 1 1 0 1 1 0 X X 0 1 X+1 1 1 1 X 1 1
0 0 1 0 0 0 1 1 1 1 X+1 0 0 X+1 X 0 X+1 1 X X+1 0 1 X 1 0 X+1 X+1 0 1 1 1 X+1 0 1 0 X X 0 1 0 X+1 X X+1 1 X+1 X X+1 1 X 1 X+1 0 0 1 1 1 1 X+1 1 0 1 X X 1 0 X+1 0 0 1 X 0 0 X+1 X 0 X+1 0 X 1 1 1
0 0 0 1 0 1 1 0 1 X X+1 1 0 1 1 X X X X+1 1 1 X+1 X X 0 0 1 0 1 0 0 1 0 0 X+1 1 1 0 X+1 1 X+1 X X X 1 X+1 1 X 0 0 1 X+1 X 0 1 0 0 X+1 1 1 0 1 1 X X+1 X+1 1 X 1 1 1 1 0 1 0 X+1 X+1 0 1 X+1 X+1
0 0 0 0 1 1 0 1 X+1 X X+1 X+1 1 X 0 1 1 0 X+1 1 X+1 1 X 0 0 1 X+1 1 X 1 1 X X+1 1 X X+1 X X+1 X+1 1 0 X+1 X X 1 X X X 1 0 X+1 0 0 X+1 X 0 X 0 X X+1 X+1 0 X+1 0 X+1 0 1 X 0 0 X+1 X+1 0 1 X X+1 X 1 X 1 1
0 0 0 0 0 X 0 0 X 0 X X X X 0 X 0 X 0 0 0 0 X X X X X X 0 X X 0 0 X 0 X X 0 X 0 X 0 0 0 X X X 0 0 0 0 X 0 0 X 0 X 0 0 X X 0 0 X 0 X X X 0 X X 0 0 0 0 X 0 X X 0 X
0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 X X X X 0 0 X 0 0 X 0 X 0 X X 0 0 X X 0 X 0 X 0 X X 0 X 0 X X 0 0 X X 0 X 0 X X X X 0 X X 0 X X X 0 0 0 X X 0 0 0 X 0 0 X X 0 X X 0
0 0 0 0 0 0 0 X 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 X X X X X X X X X X X X X X X X X X X 0 X X X X X 0 X X 0 0 X X X X 0 X X X 0 0 0 0 0 0 0 0 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+182x^70+212x^71+277x^72+316x^73+363x^74+392x^75+383x^76+438x^77+430x^78+432x^79+461x^80+408x^81+439x^82+426x^83+426x^84+446x^85+355x^86+372x^87+318x^88+242x^89+211x^90+170x^91+137x^92+88x^93+54x^94+30x^95+38x^96+18x^97+11x^98+12x^99+6x^100+6x^101+3x^102+2x^103+1x^104
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 68.1 seconds.