The generator matrix

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

generates a code of length 82 over Z2[X]/(X^2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+20x^40+34x^42+81x^44+140x^46+310x^48+480x^50+718x^52+820x^54+969x^56+1052x^58+949x^60+837x^62+685x^64+522x^66+282x^68+92x^69+168x^70+238x^71+71x^72+496x^73+40x^74+960x^75+10x^76+1518x^77+3x^78+2300x^79+2610x^81+2528x^83+2276x^85+8x^86+1594x^87+10x^88+992x^89+40x^90+500x^91+70x^92+194x^93+156x^94+60x^95+297x^96+14x^97+442x^98+12x^99+736x^100+868x^102+960x^104+1022x^106+1028x^108+866x^110+651x^112+448x^114+250x^116+184x^118+82x^120+52x^122+12x^124+4x^126+4x^130+2x^134

The gray image is a linear code over GF(2) with n=164, k=15 and d=40.
This code was found by Heurico 1.16 in 99.5 seconds.