The generator matrix

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

generates a code of length 42 over Z4 who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+60x^29+214x^30+416x^31+598x^32+938x^33+1317x^34+1784x^35+2442x^36+2982x^37+3697x^38+4660x^39+5184x^40+5402x^41+5739x^42+5622x^43+5210x^44+4662x^45+4012x^46+3228x^47+2343x^48+1746x^49+1207x^50+840x^51+546x^52+310x^53+181x^54+80x^55+58x^56+26x^57+17x^58+10x^59+2x^60+2x^61

The gray image is a code over GF(2) with n=84, k=16 and d=29.
This code was found by Heurico 1.10 in 119 seconds.