The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  1  2  2  1  4  2  1  1  4  4  1  2  0  1  1  4  0  1  1  1  1  2  4  4  1  1
 0 12  0  4  0  0  4 12  0  8  4  0  4  8  4  4  0  8  0  4 12  0  4  4  8 12  0 12  4  4  4  4 12  4 12  8  8  4  8  8  4 12  0 12  0  8  0 12 12  4  4  8  8 12
 0  0 12  4  0 12  4  0  0  4  0  8 12 12  8  4  8  4  4  4  0  8  4  0  4  8 12  8  8  4  4 12  8 12 12  0  4  4  8 12  8  0  4  0  4  4  8  0 12  0 12  4  8  0
 0  0  0  8  0  0  0  0  0  8  8  8  8  0  0  0  0  0  8  8  0  8  8  0  8  0  8  8  0  8  0  0  8  8  0  8  8  8  8  0  0  0  0  8  8  0  8  8  0  8  8  0  8  0
 0  0  0  0  8  0  0  0  0  0  0  0  8  8  8  8  8  8  0  8  0  8  0  8  0  8  0  0  0  0  8  0  8  8  8  0  0  8  0  8  0  8  8  8  8  0  8  0  8  8  8  8  0  0
 0  0  0  0  0  8  0  0  0  8  0  0  0  0  0  8  8  8  8  0  8  8  8  8  8  0  0  8  0  8  8  0  0  8  8  0  0  0  0  8  8  0  8  8  0  0  8  8  8  8  0  0  0  0
 0  0  0  0  0  0  8  0  0  8  8  8  0  0  0  0  8  8  0  8  0  8  0  8  0  8  8  0  8  0  8  0  0  8  0  0  8  0  8  0  0  0  8  0  0  8  8  8  8  8  0  0  0  0
 0  0  0  0  0  0  0  8  0  0  8  0  0  0  0  8  8  8  8  0  0  8  8  8  0  0  8  8  8  0  0  8  8  0  0  8  8  0  8  0  8  0  0  8  8  8  0  8  8  8  8  0  0  8
 0  0  0  0  0  0  0  0  8  0  0  8  0  0  0  8  8  0  0  0  8  8  0  0  0  8  0  8  8  8  8  8  0  8  8  8  8  8  0  0  0  8  8  0  0  0  0  0  8  8  0  8  8  8

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

Homogenous weight enumerator: w(x)=1x^0+102x^44+200x^46+16x^47+580x^48+272x^49+772x^50+1008x^51+2036x^52+1776x^53+2940x^54+1776x^55+2043x^56+1008x^57+756x^58+272x^59+439x^60+16x^61+172x^62+141x^64+24x^66+30x^68+3x^72+1x^76

The gray image is a code over GF(2) with n=432, k=14 and d=176.
This code was found by Heurico 1.16 in 6.12 seconds.