The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+150x^34+304x^36+316x^38+296x^40+283x^42+290x^44+194x^46+119x^48+78x^50+14x^52+2x^54+1x^58

The gray image is a code over GF(2) with n=82, k=11 and d=34.
This code was found by Heurico 1.16 in 1.62 seconds.