The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+132x^44+4x^45+332x^46+132x^47+1340x^48+1056x^49+3960x^50+3840x^51+8934x^52+7208x^53+11704x^54+7304x^55+8847x^56+3904x^57+3916x^58+992x^59+1289x^60+116x^61+296x^62+20x^63+157x^64+12x^66+28x^68+4x^70+7x^72+1x^76

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 40.3 seconds.