The generator matrix

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

generates a code of length 42 over Z4 who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+96x^32+104x^33+218x^34+308x^35+392x^36+448x^37+472x^38+546x^39+554x^40+652x^41+597x^42+614x^43+614x^44+594x^45+499x^46+482x^47+322x^48+210x^49+236x^50+94x^51+61x^52+38x^53+25x^54+4x^55+7x^56+2x^57+1x^60+1x^66

The gray image is a code over GF(2) with n=84, k=13 and d=32.
This code was found by Heurico 1.10 in 2.03 seconds.