The generator matrix

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

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+137x^68+208x^70+565x^72+604x^74+869x^76+786x^78+1054x^80+816x^82+925x^84+724x^86+688x^88+348x^90+253x^92+90x^94+69x^96+8x^98+38x^100+7x^104+2x^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 14.2 seconds.