The generator matrix

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

generates a code of length 40 over Z4 who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+63x^30+108x^31+169x^32+268x^33+371x^34+472x^35+482x^36+530x^37+649x^38+640x^39+696x^40+644x^41+563x^42+672x^43+516x^44+408x^45+321x^46+260x^47+174x^48+64x^49+73x^50+24x^51+10x^52+6x^53+7x^54+1x^58

The gray image is a code over GF(2) with n=80, k=13 and d=30.
This code was found by Heurico 1.16 in 4.7 seconds.