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
 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  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  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  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  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  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  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  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  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  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  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  0  0  X  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

generates a code of length 79 over Z2[X]/(X^2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+14x^40+24x^42+150x^44+260x^46+476x^48+664x^50+897x^52+1075x^54+1080x^56+1136x^58+854x^60+630x^62+461x^64+354x^66+363x^68+541x^70+898x^72+1764x^74+2056x^76+2762x^78+2464x^80+2334x^82+1504x^84+1050x^86+536x^88+362x^90+357x^92+449x^94+625x^96+871x^98+1045x^100+1137x^102+1089x^104+930x^106+705x^108+401x^110+237x^112+135x^114+50x^116+15x^118+7x^120+2x^122+2x^124+1x^132

The gray image is a linear code over GF(2) with n=158, k=15 and d=40.
This code was found by Heurico 1.16 in 99.7 seconds.