The generator matrix

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

generates a code of length 52 over Z16 who´s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+234x^47+1021x^48+1564x^49+2223x^50+2002x^51+2794x^52+1834x^53+2093x^54+1262x^55+744x^56+308x^57+161x^58+66x^59+38x^60+22x^61+3x^62+4x^63+10x^64

The gray image is a code over GF(2) with n=416, k=14 and d=188.
This code was found by Heurico 1.16 in 1.99 seconds.