The generator matrix

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

generates a code of length 41 over Z4 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+130x^28+160x^29+483x^30+580x^31+1070x^32+1166x^33+1963x^34+2312x^35+3022x^36+3794x^37+4398x^38+5330x^39+5299x^40+5888x^41+5216x^42+5518x^43+4498x^44+3864x^45+3203x^46+2396x^47+1909x^48+1106x^49+967x^50+472x^51+414x^52+134x^53+140x^54+30x^55+41x^56+16x^57+14x^58+2x^59

The gray image is a code over GF(2) with n=82, k=16 and d=28.
This code was found by Heurico 1.10 in 110 seconds.