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

generates a code of length 81 over Z4 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+23x^40+42x^42+141x^44+263x^46+419x^48+697x^50+873x^52+1123x^54+1026x^56+1126x^58+876x^60+657x^62+474x^64+253x^66+233x^68+337x^70+481x^72+976x^74+1625x^76+2168x^78+2568x^80+2558x^82+2164x^84+1612x^86+1036x^88+542x^90+264x^92+189x^94+278x^96+445x^98+694x^100+894x^102+1025x^104+1136x^106+1038x^108+984x^110+612x^112+487x^114+230x^116+122x^118+38x^120+26x^122+6x^124+3x^126+2x^128+1x^136

The gray image is a code over GF(2) with n=162, k=15 and d=40.
This code was found by Heurico 1.16 in 97.9 seconds.