The generator matrix

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

generates a code of length 41 over Z4 who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+172x^34+265x^36+328x^38+321x^40+239x^42+293x^44+223x^46+130x^48+57x^50+14x^52+5x^54

The gray image is a code over GF(2) with n=82, k=11 and d=34.
This code was found by Heurico 1.10 in 0.125 seconds.