The generator matrix

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

generates a code of length 86 over Z2[X]/(X^2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+30x^40+30x^42+99x^44+113x^46+229x^48+427x^50+499x^52+710x^54+938x^56+966x^58+975x^60+956x^62+754x^64+575x^66+423x^68+256x^70+172x^72+214x^74+378x^76+731x^78+1198x^80+1846x^82+2538x^84+2640x^86+2456x^88+1970x^90+1222x^92+710x^94+358x^96+184x^98+166x^100+288x^102+430x^104+559x^106+749x^108+933x^110+990x^112+1032x^114+929x^116+674x^118+490x^120+389x^122+246x^124+147x^126+85x^128+24x^130+23x^132+10x^134+4x^136+1x^140+1x^144

The gray image is a linear code over GF(2) with n=172, k=15 and d=40.
This code was found by Heurico 1.16 in 99.8 seconds.