The generator matrix

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

generates a code of length 53 over Z16 who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+180x^46+368x^47+935x^48+1700x^49+2512x^50+3880x^51+4316x^52+5044x^53+4464x^54+3928x^55+2443x^56+1564x^57+726x^58+328x^59+183x^60+76x^61+74x^62+8x^63+23x^64+10x^66+1x^68+2x^70+2x^72

The gray image is a code over GF(2) with n=424, k=15 and d=184.
This code was found by Heurico 1.16 in 10.4 seconds.