The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+63x^44+84x^45+231x^46+394x^47+764x^48+1696x^49+2851x^50+4778x^51+7291x^52+9364x^53+10496x^54+9620x^55+7187x^56+4764x^57+2777x^58+1564x^59+792x^60+360x^61+194x^62+82x^63+84x^64+52x^65+24x^66+10x^67+10x^68+3x^70

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 41.4 seconds.