The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+44x^44+70x^45+171x^46+382x^47+761x^48+1576x^49+2053x^50+4518x^51+3595x^52+6420x^53+3726x^54+4464x^55+2075x^56+1584x^57+635x^58+344x^59+158x^60+70x^61+59x^62+18x^63+18x^64+8x^65+7x^66+2x^67+3x^68+4x^70+1x^72+1x^74

The gray image is a code over GF(2) with n=424, k=15 and d=176.
This code was found by Heurico 1.16 in 10.5 seconds.