The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2 12  1  4  1  4  4  1  2  4  1  2 12  0  1  2  1  1  8  1  1 12  0  1  1  1  1
 0  2  0  2  0  0 14 14  4  6  2  4 12 10 14  4  0 12  4  8 14  0  2 10  4 14 10  2  2  2 12  4  2 10  8  2  2 10 12  8  8  6  2 10  2  0  8  2  2  0 12  6  8
 0  0  2  2 12  6  6  4  4  0  6 10  8  4 10 10 10  4  0  6  8  2  2 14 10  8  8  8  8  8  4  2  6  6 14 12 10  4  2  2 12 10  4  6  2  8 10  6  2  8  2 12  8
 0  0  0  4  0  0  4  8  0  0 12  8  0  8 12  0  8  4 12  4 12  4  8  0  4  4  0  8  4  4 12  8 12  4  0  0  8  4  0  8  4  4  0  8  0  4  8  4 12  8 12 12 12
 0  0  0  0  8  0  0  0  0  8  8  8  8  8  8  8  0  0  0  0  8  8  0  8  8  8  0  8  0  8  8  0  0  0  0  0  8  0  8  8  8  0  0  0  0  8  8  0  0  0  8  0  8
 0  0  0  0  0  8  8  8  8  8  0  8  8  0  8  0  8  0  8  8  8  0  8  0  8  8  8  0  8  0  0  8  8  8  0  0  8  8  8  0  8  8  8  0  0  8  8  8  0  8  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+149x^46+316x^47+489x^48+884x^49+1117x^50+1952x^51+2087x^52+2604x^53+2136x^54+1778x^55+1121x^56+764x^57+393x^58+292x^59+129x^60+94x^61+35x^62+14x^63+9x^64+4x^65+9x^66+4x^68+2x^69+1x^74

The gray image is a code over GF(2) with n=424, k=14 and d=184.
This code was found by Heurico 1.16 in 4.17 seconds.