The generator matrix

1 0 0 0 0 0 1 1 1 X 0 0 0 0 1 1 1 X 0 X 1 1 1 1 1 0 1 1 0 1 1 1 1 0 X 0 X 1 0 1 X 0 1 1 1 1 1 1 1 1 X 1 0 X 1 1 1 0 X X 0 1 1 X X 0 X X 1 1 1 0 0 0 0 1 1 0 1 X 1
0 1 0 0 0 0 0 0 0 0 1 X 1 1 0 X X+1 X 1 1 1 0 1 X+1 X+1 0 X+1 X+1 1 1 X X X+1 1 1 1 1 1 1 0 1 X X+1 0 X+1 0 X 1 X+1 0 1 1 X 1 X 1 X+1 1 0 0 X 1 X X 1 1 0 0 0 X+1 1 0 1 1 X X 0 1 0 1 0
0 0 1 0 0 0 0 0 0 0 X 1 1 X+1 X+1 1 1 1 1 X 1 X+1 0 X X 1 0 1 1 0 X+1 1 X+1 0 X+1 X 0 X+1 X+1 X 0 0 X+1 X+1 0 X X 1 0 X X 0 X X+1 X+1 X+1 X X X X X X+1 0 0 X+1 X 0 1 X+1 1 0 1 0 X+1 0 X 0 X+1 1 1 1
0 0 0 1 0 0 0 1 1 1 1 1 0 1 X X+1 0 1 X 0 X 1 X 1 X+1 X 0 X+1 X+1 X+1 X X X+1 0 0 1 X X+1 1 1 1 X X 0 1 0 X X X 1 X+1 X+1 X X 0 X+1 1 X 1 1 1 X+1 0 0 0 X 0 0 X 1 1 0 X 0 1 0 0 X 1 X X
0 0 0 0 1 0 1 0 X+1 1 1 1 X X+1 1 X 1 X X+1 1 0 X+1 X+1 0 X+1 X+1 X 0 X 1 0 1 X+1 0 X X X+1 0 1 X 1 1 X X 0 X+1 X X+1 X X+1 X+1 X+1 1 1 0 X X+1 0 1 X+1 1 0 1 1 X+1 X+1 0 X+1 X X+1 0 X X 1 0 1 X 1 X 1 1
0 0 0 0 0 1 1 X+1 X 1 0 X 1 X+1 X 0 X+1 X+1 0 X+1 0 1 X 0 1 X+1 X+1 X+1 X X+1 X+1 X 0 0 X+1 1 1 1 X+1 1 X X X+1 0 1 0 X+1 X X X+1 X+1 X 1 X+1 X 0 0 X+1 0 X X+1 X 1 1 0 0 1 X X X X X X+1 0 1 X+1 1 0 X X+1 X
0 0 0 0 0 0 X X 0 0 0 0 0 0 X X X 0 0 0 X X X X X 0 X 0 X 0 X 0 0 X X X X X X 0 X X 0 0 0 0 0 0 X 0 X 0 X X X X 0 X 0 X X 0 0 X X X X X 0 X 0 X 0 0 X X X X X X X

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+72x^69+160x^70+248x^71+280x^72+340x^73+355x^74+392x^75+389x^76+362x^77+503x^78+412x^79+467x^80+446x^81+424x^82+426x^83+389x^84+444x^85+352x^86+360x^87+276x^88+264x^89+212x^90+172x^91+162x^92+98x^93+87x^94+36x^95+16x^96+22x^97+16x^98+2x^99+3x^100+2x^102+1x^106+1x^108

The gray image is a linear code over GF(2) with n=162, k=13 and d=69.
This code was found by Heurico 1.10 in 4.08 seconds.