The generator matrix

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

generates a code of length 81 over Z2[X]/(X^2) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+61x^68+74x^69+136x^70+210x^71+337x^72+306x^73+341x^74+390x^75+343x^76+394x^77+454x^78+492x^79+401x^80+454x^81+427x^82+458x^83+420x^84+420x^85+348x^86+310x^87+315x^88+282x^89+241x^90+134x^91+132x^92+102x^93+82x^94+44x^95+34x^96+14x^97+13x^98+10x^99+3x^100+2x^101+4x^102+2x^106+1x^108

The gray image is a linear code over GF(2) with n=162, k=13 and d=68.
This code was found by Heurico 1.16 in 13.9 seconds.