The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+130x^47+379x^48+940x^49+1734x^50+2554x^51+3696x^52+4832x^53+4710x^54+4528x^55+3660x^56+2654x^57+1366x^58+778x^59+440x^60+168x^61+106x^62+42x^63+28x^64+10x^65+4x^66+4x^68+4x^69

The gray image is a code over GF(2) with n=432, k=15 and d=188.
This code was found by Heurico 1.16 in 10.1 seconds.