The generator matrix

 1  0  0  0  0  0  1  1  1  1  1  1  1  0  1  1  0  1  1  2  0  1  1  0  0  0  1  1  2  2  0  0  2  1  2  2  1  1  1  1  1  1  0  0  1  0  1  1  2  2  2  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  3  0  1  2  2  0  3  1  2  0  1  1  1  3  0  1  2  1  2  1  1  2  2  1  0  2  1  0  0  2  0  1  3  0  1  3  1  2  3  2  1  1  0  0  2  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  2  2  2  3  1  1  3  2  2  2  1  2  1  2  1  2  1  0  3  1  2  1  1  2  3  0  1  1  3  2  0  0  0  2  1  1  1  1  0  2  0  0  2  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  2  1  1  0  3  0  3  2  2  0  0  3  0  3  0  3  1  1  0  3  2  1  1  0  0  2  0  2  0  2  1  2  1  0  0  0  1  3  2  2  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  2  2  0  3  3  2  2  3  3  2  1  3  2  2  2  3  0  1  2  0  2  2  1  0  3  0  2  1  2  2  3  1  0  1  0  1  1  2  3  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  2  0  1  3  0  2  3  2  0  2  2  1  1  0  1  3  2  0  0  0  0  1  3  1  2  0  3  0  2  0  3  2  0  1  1  3  1  1  1  3  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  2  0  0  0  2  2  2  0  2  0  2  2  0  2  0  2  0  2  0  0  0  0  2  2  2  2  0  0  2  0  2  0  0  2  2  2  0  0  2  0  2  0  2  2  0  2  2  2  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  2  0  2  2  2  0  0  0  0  0  2  2  2  2  0  2  0  2  0  2  2  0  2  0  2  2  2  0  0  0  0  0  2  0  0  2  0  0  0  2  2  0  2  0  0  2  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  2  2  0  0  2  2  2  0  0  2  2  2  0  2  0  0  2  0  2  2  2  0  0  2  0  0  2  0  0  0  2  2  2  2  2  2  2  2  0  2  0  2  0  2  0  2  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 Z4 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+37x^40+54x^41+81x^42+108x^43+158x^44+202x^45+268x^46+288x^47+394x^48+436x^49+491x^50+610x^51+598x^52+670x^53+646x^54+646x^55+516x^56+440x^57+406x^58+354x^59+370x^60+328x^61+370x^62+344x^63+467x^64+626x^65+729x^66+836x^67+892x^68+1016x^69+1122x^70+1234x^71+1289x^72+1210x^73+1135x^74+1080x^75+928x^76+878x^77+680x^78+560x^79+427x^80+330x^81+370x^82+338x^83+386x^84+378x^85+435x^86+456x^87+497x^88+556x^89+593x^90+664x^91+660x^92+604x^93+544x^94+424x^95+427x^96+336x^97+231x^98+216x^99+116x^100+116x^101+79x^102+32x^103+25x^104+12x^105+11x^106+2x^107+4x^108+1x^114

The gray image is a code over GF(2) with n=144, k=15 and d=40.
This code was found by Heurico 1.16 in 99.7 seconds.