The generator matrix

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

generates a code of length 40 over Z4 who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+43x^26+8x^27+118x^28+30x^29+215x^30+106x^31+354x^32+318x^33+574x^34+766x^35+902x^36+1280x^37+1181x^38+1572x^39+1314x^40+1628x^41+1281x^42+1284x^43+972x^44+702x^45+569x^46+338x^47+328x^48+134x^49+177x^50+22x^51+86x^52+4x^53+51x^54+18x^56+4x^58+2x^60+1x^64+1x^66

The gray image is a code over GF(2) with n=80, k=14 and d=26.
This code was found by Heurico 1.16 in 17.2 seconds.