The generator matrix

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

generates a code of length 54 over Z16 who´s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+124x^47+695x^48+1726x^49+3187x^50+5670x^51+7002x^52+9726x^53+9508x^54+9768x^55+7209x^56+5414x^57+2781x^58+1528x^59+719x^60+298x^61+103x^62+28x^63+19x^64+20x^65+4x^66+2x^67+3x^68+1x^70

The gray image is a code over GF(2) with n=432, k=16 and d=188.
This code was found by Heurico 1.16 in 31 seconds.