The generator matrix

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

generates a code of length 42 over Z4 who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+46x^31+149x^32+294x^33+428x^34+496x^35+617x^36+858x^37+970x^38+1052x^39+1189x^40+1252x^41+1418x^42+1456x^43+1224x^44+1128x^45+1071x^46+834x^47+658x^48+482x^49+294x^50+188x^51+119x^52+78x^53+38x^54+20x^55+11x^56+4x^57+4x^58+4x^59+1x^62

The gray image is a code over GF(2) with n=84, k=14 and d=31.
This code was found by Heurico 1.10 in 7.59 seconds.