The generator matrix

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

generates a code of length 43 over Z4 who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+88x^30+156x^31+464x^32+668x^33+1025x^34+1270x^35+1926x^36+2318x^37+3102x^38+3888x^39+4295x^40+5044x^41+5189x^42+5844x^43+5608x^44+5380x^45+4664x^46+3826x^47+3135x^48+2440x^49+1824x^50+1210x^51+938x^52+490x^53+326x^54+176x^55+137x^56+40x^57+33x^58+12x^59+8x^60+4x^61+4x^62+2x^63+1x^66

The gray image is a code over GF(2) with n=86, k=16 and d=30.
This code was found by Heurico 1.10 in 117 seconds.