The generator matrix

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

generates a code of length 41 over Z4 who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+54x^31+138x^32+206x^33+311x^34+312x^35+379x^36+488x^37+538x^38+664x^39+670x^40+694x^41+661x^42+604x^43+589x^44+480x^45+438x^46+370x^47+234x^48+154x^49+91x^50+44x^51+31x^52+24x^53+8x^54+4x^56+2x^57+1x^58+1x^60+1x^64

The gray image is a code over GF(2) with n=82, k=13 and d=31.
This code was found by Heurico 1.10 in 1.96 seconds.