The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+66x^30+82x^31+182x^32+328x^33+346x^34+408x^35+465x^36+584x^37+674x^38+596x^39+701x^40+708x^41+574x^42+600x^43+493x^44+460x^45+336x^46+218x^47+179x^48+84x^49+48x^50+16x^51+25x^52+12x^53+4x^54+1x^56+1x^60

The gray image is a code over GF(2) with n=80, k=13 and d=30.
This code was found by Heurico 1.10 in 1.89 seconds.