The generator matrix

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

generates a code of length 72 over Z2[X]/(X^2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+28x^40+50x^41+91x^42+134x^43+163x^44+212x^45+269x^46+320x^47+404x^48+462x^49+482x^50+594x^51+607x^52+588x^53+630x^54+562x^55+508x^56+444x^57+392x^58+396x^59+331x^60+342x^61+336x^62+352x^63+477x^64+576x^65+632x^66+806x^67+1011x^68+1072x^69+1086x^70+1216x^71+1428x^72+1328x^73+1137x^74+1102x^75+1018x^76+840x^77+667x^78+590x^79+472x^80+322x^81+318x^82+308x^83+320x^84+342x^85+414x^86+454x^87+506x^88+632x^89+586x^90+598x^91+590x^92+544x^93+580x^94+508x^95+398x^96+324x^97+220x^98+200x^99+142x^100+106x^101+78x^102+44x^103+34x^104+6x^105+14x^106+6x^107+10x^108+2x^109+4x^110+2x^111

The gray image is a linear code over GF(2) with n=144, k=15 and d=40.
This code was found by Heurico 1.16 in 99.9 seconds.