The generator matrix

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

generates a code of length 43 over Z4 who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+296x^34+594x^36+893x^38+1024x^40+1256x^42+1282x^44+1190x^46+821x^48+516x^50+235x^52+69x^54+10x^56+4x^58+1x^68

The gray image is a code over GF(2) with n=86, k=13 and d=34.
This code was found by Heurico 1.16 in 11.2 seconds.