The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+208x^46+676x^47+1692x^48+3012x^49+5345x^50+7228x^51+9682x^52+9844x^53+9796x^54+7460x^55+5242x^56+2828x^57+1479x^58+628x^59+250x^60+60x^61+52x^62+8x^63+25x^64+15x^66+4x^68+1x^74

The gray image is a code over GF(2) with n=424, k=16 and d=184.
This code was found by Heurico 1.16 in 33.3 seconds.