The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+67x^44+110x^45+183x^46+376x^47+799x^48+1662x^49+2767x^50+4762x^51+7331x^52+9422x^53+10282x^54+9582x^55+7822x^56+4806x^57+2542x^58+1530x^59+649x^60+364x^61+187x^62+130x^63+90x^64+20x^65+35x^66+4x^67+9x^68+4x^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 40.7 seconds.