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

generates a code of length 79 over Z4 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+15x^40+18x^41+54x^42+52x^43+107x^44+110x^45+193x^46+212x^47+282x^48+310x^49+354x^50+470x^51+476x^52+550x^53+541x^54+646x^55+560x^56+560x^57+513x^58+426x^59+401x^60+376x^61+266x^62+202x^63+141x^64+124x^65+160x^66+110x^67+204x^68+202x^69+299x^70+402x^71+495x^72+628x^73+791x^74+934x^75+1080x^76+1178x^77+1273x^78+1324x^79+1250x^80+1232x^81+1026x^82+926x^83+840x^84+660x^85+532x^86+368x^87+268x^88+190x^89+182x^90+108x^91+159x^92+124x^93+158x^94+240x^95+306x^96+316x^97+432x^98+474x^99+409x^100+540x^101+558x^102+628x^103+567x^104+600x^105+444x^106+412x^107+412x^108+360x^109+305x^110+214x^111+166x^112+86x^113+78x^114+40x^115+47x^116+28x^117+26x^118+4x^119+5x^120+6x^122+1x^124+1x^126

The gray image is a code over GF(2) with n=158, k=15 and d=40.
This code was found by Heurico 1.16 in 99.7 seconds.