The generator matrix

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

generates a code of length 53 over Z4 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+144x^40+156x^41+359x^42+478x^43+713x^44+836x^45+1112x^46+1336x^47+1598x^48+1826x^49+1950x^50+2208x^51+2114x^52+2490x^53+2487x^54+2390x^55+2083x^56+2020x^57+1661x^58+1338x^59+1053x^60+716x^61+610x^62+384x^63+299x^64+142x^65+117x^66+56x^67+56x^68+6x^69+23x^70+2x^71+3x^72+1x^82

The gray image is a code over GF(2) with n=106, k=15 and d=40.
This code was found by Heurico 1.10 in 42.3 seconds.