The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  8  2  0  1 12  1  2  0  1  2  2  1  1  8  1  4  2  4  2  1  1  1  8  1  1  2  8  1  1  1  2  1
 0  2  0  2  0  0  2  6  4 10  4  6 14  0  8 10  6 12  6  8 14 12  2 14  2  6  8  2  8  2 12  8  2 12  2  2 12  4  2  2  6  2  8  2  2  2 10  0  2 12 12  0  2  8
 0  0  2  2  0  6  2  4  0  2  2  8 10  0 10  4 14 12  4  2  8  2 10  2  4  8  2 14 14  0  0 10  4  0 10 14 10  2  0  2 10 12 14 10 12 14 10 10  8  6 12  0  6  0
 0  0  0  4  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8 12  4  4  4 12 12 12  4  0 12  4 12  8  0 12  4  4  4 12  8  8  0  4  8  4  4  0  8  8  0  4  4  4  4  0
 0  0  0  0 12  0  0  0  0  0 12 12  4 12  4 12 12  0  8 12  8 12  4  0  4  4  4  4  0  8  4  0  8  8  4  4  0  4 12 12  4 12 12  4  4  4  8  0  8  0  8  8 12 12
 0  0  0  0  0 12  8 12  4 12 12 12  0  4  0  8 12  8  8  8  8  4  8 12  4  8  8  4  4  4 12  4  0  0  4 12  0  4 12  4  4 12  8 12  8  8  8 12 12  4 12  4  4  0

generates a code of length 54 over Z16 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+85x^44+152x^45+364x^46+698x^47+1086x^48+1808x^49+3210x^50+4828x^51+6791x^52+8994x^53+9499x^54+8886x^55+7227x^56+4800x^57+2969x^58+1736x^59+1114x^60+580x^61+303x^62+222x^63+74x^64+48x^65+33x^66+12x^67+6x^68+2x^69+6x^70+2x^71

The gray image is a code over GF(2) with n=432, k=16 and d=176.
This code was found by Heurico 1.16 in 58.2 seconds.