The generator matrix

 1  0  0  0  0  1  1  1  1  1  1  1  X  X  X  0  0  X  0  X  X  X  0  1  1  0  X  1  1  1  1  1  0  0  1  1  1  X  X  1  0  X  X  X  0  1  1  X  0  1  X  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  0  1  X  0  X  X  X  0  1 X+1  X  X  1 X+1  0  1  0  X  X  1  0  1  0  X  X  0  0  1  1  X  X X+1  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 X+1  X  1  0  1  0  1  X  0  1  X X+1  1  X  0  X  0 X+1  1  X  X  1  1 X+1 X+1  1  X X+1  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  1  0  1  1  1  0  0  0  1  1  0  0 X+1 X+1  0 X+1 X+1 X+1 X+1  X X+1 X+1  1 X+1  0  X  1  1 X+1  1  X  X  0 X+1  0  1  1  X  X X+1  1  X  X X+1  1  1 X+1  X  X  0  1  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  X  X  X X+1  1  1  0  0  X X+1  X X+1  1  1  1  X  0 X+1  0 X+1  1  0  X  0  1  1 X+1  X  1  1  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  X  0  0  0  0  0  X  0  X  X  0  X  0  X  X  X  0  X  0  X  X  X  0  X  X  0  X  X  0  X  X  X  0  X  X  X  0  X  0  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  X  0  0  0  0  X  X  X  0  0  X  X  0  0  X  X  0  0  X  X  X  X  X  X  X  0  0  X  0  X  X  0  X  X  0  0  0  0  X  X  X  0  0  0  X  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  X  0  0  X  0  X  0  X  0  X  0  X  0  X  X  0  0  0  X  0  0  X  0  X  X  X  0  0  0  0  X  X  X  X  X  X  0  0  X  X  X  X  0  X  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  X  0  X  0  0  X  X  X  0  0  X  X  0  X  0  X  X  0  0  X  0  X  X  X  0  0  X  0  0  0  X  X  0  X  X  0  0  0  X  X  X  X  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  X  0  X  X  0  X  X  X  0  0  X  0  X  0  0  X  0  0  0  0  X  X  X  X  X  X  X  0  X  0  X  0  0  X  0  X  X  0  X  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+20x^40+50x^41+80x^42+114x^43+170x^44+200x^45+261x^46+356x^47+382x^48+444x^49+544x^50+580x^51+609x^52+632x^53+606x^54+534x^55+534x^56+498x^57+386x^58+398x^59+348x^60+342x^61+370x^62+390x^63+470x^64+558x^65+718x^66+854x^67+861x^68+986x^69+1178x^70+1184x^71+1240x^72+1306x^73+1146x^74+1046x^75+1057x^76+840x^77+691x^78+576x^79+445x^80+382x^81+316x^82+320x^83+320x^84+352x^85+396x^86+480x^87+547x^88+538x^89+677x^90+686x^91+625x^92+612x^93+459x^94+452x^95+396x^96+348x^97+268x^98+158x^99+130x^100+98x^101+86x^102+58x^103+27x^104+4x^105+9x^106+4x^107+8x^108+2x^109+1x^110+2x^111+2x^112

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 98.5 seconds.