The generator matrix

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

generates a code of length 82 over Z2[X]/(X^2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+176x^72+380x^74+478x^76+498x^78+445x^80+448x^82+382x^84+348x^86+310x^88+242x^90+168x^92+104x^94+74x^96+26x^98+12x^100+2x^102+2x^104

The gray image is a linear code over GF(2) with n=164, k=12 and d=72.
This code was found by Heurico 1.16 in 3.16 seconds.