The generator matrix

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

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+26x^40+71x^42+170x^44+302x^46+553x^48+773x^50+1035x^52+1170x^54+1187x^56+1023x^58+769x^60+526x^62+292x^64+267x^66+229x^68+456x^70+727x^72+1244x^74+1979x^76+2310x^78+2530x^80+2326x^82+1936x^84+1330x^86+700x^88+454x^90+217x^92+241x^94+309x^96+531x^98+764x^100+1022x^102+1231x^104+1207x^106+1016x^108+721x^110+527x^112+328x^114+140x^116+64x^118+45x^120+15x^122+1x^124+2x^126+1x^130

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 99.8 seconds.