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  2  0  0  1  2  2  2  1  2  1  1  0  0  1  1  2  0  1  0  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
 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  1  2  0  1  2  1  2  1  0  2  3  0  1  2  3  1  1  3  0  1  1  0  1  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  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  2  1  1  0  0  2  1  3  1  2  3  2  0  2  2  1  0  0  1  2  1  2  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  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  2  0  0  2  1  3  0  3  2  0  1  2  1  0  3  3  2  2  3  0  1  2  1  0  0  0  0  0  2  0  0  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  1  0  1  1  0  0  0  1  1  1  2  2  0  3  3  2  2  3  3  2  1  1  3  1  1  1  1  1  0  1  0  0  1  3  1  2  0  0  0  3  3  0  2  1  0  1  0  2  0  2  0  0  2  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  0  1  1  1  0  1  1  2  0  1  3  0  2  3  2  0  2  2  1  1  0  2  1  1  1  3  0  1  2  0  1  1  0  1  2  0  2  1  3  1  3  3  0  1  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  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  0  2  2  0  2  2  2  0  0  0  0  0  2  2  0  2  0  2  0  0  2  2  0  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  0  0  0  0  0  2  0  2  2  2  0  0  0  0  0  2  2  2  2  0  2  0  2  0  0  0  2  2  0  2  0  2  0  2  0  2  2  2  2  0  0  0  2  0  0  0  2  2  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  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  2  0  2  2  0  2  2  2  0  0  2  0  2  0  0  0  2  0  0  2  2  2  0  0  0  2  2  0  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

generates a code of length 82 over Z4 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+36x^40+46x^42+159x^44+263x^46+458x^48+662x^50+880x^52+1044x^54+1147x^56+949x^58+923x^60+655x^62+443x^64+288x^66+184x^68+220x^70+361x^72+673x^74+1302x^76+1864x^78+2468x^80+2664x^82+2448x^84+1998x^86+1282x^88+696x^90+310x^92+200x^94+204x^96+261x^98+476x^100+600x^102+864x^104+1046x^106+1136x^108+1009x^110+948x^112+734x^114+418x^116+203x^118+132x^120+44x^122+52x^124+7x^126+8x^128+1x^130+1x^134

The gray image is a code over GF(2) with n=164, k=15 and d=40.
This code was found by Heurico 1.16 in 99.6 seconds.