The generator matrix

 1  0  1  1  1 14  1  1  4  1  1  4 10  1  1  1 12  1  6  1  1  1  6  1  1  1  4  1  1  1  1  1  1 14  1  2  1  2  1  2  1  4  1  1  1  1  2  1  1  1  1  8  1  2
 0  1  1  0  7  1  2  3  1  6  5  1  1  4 10 15  1 15  1  8 10  5  1  1 14 15  1  0  7  9  8  7  6  1  2  1 11  1  4  1  4  1  3 10  1 15  0 11  4 14 12  1  7  2
 0  0  2  6  2  4 14  0  2  0  8  4  6  6 10  8  6  6  6  4  0  4  4 14  8 12  6  4 10 12 10  0 12 14 10  0 10 14  0  4  6 12  6 12  0  4  6 12 10 14 10 12  6  6
 0  0  0 12  0  0 12  8  0  8  0  8  0  4 12  0  8  8  8  0  0 12 12  4 12 12 12 12 12  4  8  4  0  4  8 12 12 12 12  4  0  8  8 12 12  8  0 12  8  8  8  8 12 12
 0  0  0  0  8  0  8  0  8  8  8  8  0  8  0  8  0  0  8  0  8  8  0  0  0  0  8  8  8  0  0  8  0  0  8  8  8  0  8  8  8  8  8  8  0  0  8  0  8  0  0  0  0  0
 0  0  0  0  0  8  0  0  0  0  0  8  0  8  8  8  8  8  8  8  8  8  0  0  8  0  0  0  0  8  8  0  0  8  8  8  8  0  0  0  8  0  8  8  0  8  0  8  0  8  0  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+148x^47+400x^48+700x^49+1567x^50+2854x^51+3506x^52+4588x^53+5498x^54+4610x^55+3525x^56+2440x^57+1483x^58+858x^59+295x^60+134x^61+82x^62+36x^63+10x^64+8x^65+9x^66+4x^67+7x^68+2x^69+2x^71+1x^74

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 10.6 seconds.