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

generates a code of length 80 over Z2[X]/(X^2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+18x^40+42x^42+108x^44+183x^46+385x^48+595x^50+731x^52+1015x^54+1007x^56+1026x^58+964x^60+769x^62+654x^64+4x^65+361x^66+94x^67+187x^68+226x^69+85x^70+498x^71+39x^72+872x^73+14x^74+1760x^75+2x^76+2054x^77+4x^78+2762x^79+2462x^81+2x^82+2334x^83+1502x^85+12x^86+1030x^87+46x^88+484x^89+122x^90+212x^91+212x^92+74x^93+346x^94+14x^95+540x^96+2x^97+738x^98+1024x^100+1080x^102+1093x^104+957x^106+699x^108+605x^110+341x^112+188x^114+118x^116+43x^118+17x^120+3x^122+3x^124+1x^126+3x^128+1x^134

The gray image is a linear code over GF(2) with n=160, k=15 and d=40.
This code was found by Heurico 1.16 in 99.1 seconds.