The generator matrix

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

generates a code of length 42 over Z4 who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+68x^30+188x^31+338x^32+522x^33+767x^34+902x^35+1194x^36+1530x^37+1913x^38+2132x^39+2398x^40+2798x^41+2860x^42+2878x^43+2526x^44+2364x^45+2026x^46+1660x^47+1331x^48+814x^49+571x^50+378x^51+254x^52+154x^53+105x^54+52x^55+20x^56+10x^57+10x^58+2x^59+2x^60

The gray image is a code over GF(2) with n=84, k=15 and d=30.
This code was found by Heurico 1.10 in 29.8 seconds.