The generator matrix

1 0 0 0 0 0 1 1 1 2 0 1 1 1 2 1 1 0 0 1 2 1 1 0 1 0 1 2 2 1 0 0 2 1 1 0 1 1 1 0 2 0 2
0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 2 1 1 1 2 2 0 2 0 2 1 1 0 1 1 1 1 3 2 2 1 0 0 2 1 0 1
0 0 1 0 0 0 0 0 0 0 0 1 0 1 3 3 3 2 2 1 1 0 2 2 3 1 2 0 1 0 3 2 1 0 3 1 1 1 2 1 0 1 3
0 0 0 1 0 0 0 1 1 1 2 0 0 0 0 0 0 2 1 1 1 0 2 1 3 2 1 3 3 2 3 3 3 2 3 3 2 1 1 3 0 0 2
0 0 0 0 1 0 1 0 1 3 2 2 2 0 2 3 1 1 3 1 0 2 1 1 0 3 3 2 1 3 2 3 3 3 0 2 1 0 2 1 3 3 2
0 0 0 0 0 1 1 3 2 1 1 1 3 2 1 1 0 1 2 0 3 2 3 3 2 3 1 3 2 0 2 3 1 3 0 2 2 3 2 2 2 1 1
0 0 0 0 0 0 2 2 0 2 2 0 0 0 0 2 0 2 2 2 0 2 0 0 2 0 0 0 0 0 2 2 0 2 2 0 2 0 2 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+299x^34+615x^36+786x^38+1141x^40+1256x^42+1242x^44+1184x^46+849x^48+495x^50+239x^52+70x^54+8x^56+6x^58+1x^72

The gray image is a code over GF(2) with n=86, k=13 and d=34.
This code was found by Heurico 1.10 in 631 seconds.