The generator matrix

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

generates a code of length 53 over Z4 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+149x^44+374x^46+513x^48+578x^50+495x^52+488x^54+526x^56+428x^58+287x^60+158x^62+72x^64+18x^66+5x^68+4x^70

The gray image is a code over GF(2) with n=106, k=12 and d=44.
This code was found by Heurico 1.10 in 0.641 seconds.