The generator matrix

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

generates a code of length 41 over Z4 who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+68x^30+312x^32+608x^34+812x^36+1070x^38+1226x^40+1170x^42+1147x^44+890x^46+516x^48+262x^50+72x^52+28x^54+8x^56+1x^60+1x^64

The gray image is a code over GF(2) with n=82, k=13 and d=30.
This code was found by Heurico 1.10 in 1.89 seconds.