The generator matrix

 1  0  1  1  1  6  1  1  0  1 14  1  1  8  1  6  1  1  1  1  0  1  6  1  1  1  1  6  1  4  1  1  1 12  1  1  4  1  1  1  1 12  2  1  8  1  1  2  1  1 14  2  0
 0  1 11  6  1  1  8  5  1 10  1  3  3  1  6  1 13  8  6  9  1 14  1 11  8  0 11  1  6  1  7  6  4  1  5  1  1 10  1  7  1  1  1 15  1  7  8  2  3  9  1  0  1
 0  0 12  0  0  0  0  0  0  0  0 12 12 12 12 12 12  4  4  8 12 12  8  8  8  4  4 12  8  0  4 12 12  8  4  0  8  4  0  0 12  8 12  8  0 12 12  8  8  8  0  8  4
 0  0  0 12  0  0  0  0  4 12 12  0 12 12  0  4 12  8 12 12  8 12  8  0  4 12  0  8  4  0 12  0  8  4  8  8  8  4 12  8  8 12 12  4  4  4  8  8 12 12  4 12  4
 0  0  0  0  4  0  8  4  0  8  0  0  8  4  4  4  8  4 12  4 12 12  8  8  4  8 12  8 12  4  4  0  0 12  4 12 12  8  8  0 12  0  0  8 12 12  4  4  8  4  8  8  4
 0  0  0  0  0 12 12  4 12  4  8 12  8  0  0  4 12 12  4  8  0  8  8  4  4 12  4 12  0  8  8  4  8  0  8  0  0 12  8  0  4  4  4 12 12  4  4 12 12  0  0 12  4

generates a code of length 53 over Z16 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+149x^44+64x^45+548x^46+476x^47+1630x^48+2256x^49+4868x^50+7212x^51+10339x^52+10700x^53+10134x^54+7176x^55+4877x^56+2344x^57+1558x^58+428x^59+455x^60+60x^61+158x^62+4x^63+75x^64+14x^66+9x^68+1x^72

The gray image is a code over GF(2) with n=424, k=16 and d=176.
This code was found by Heurico 1.16 in 41.7 seconds.