The generator matrix

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

generates a code of length 52 over Z16 who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+380x^46+1888x^47+3300x^48+6228x^49+6920x^50+9434x^51+9174x^52+9952x^53+7157x^54+5720x^55+2799x^56+1720x^57+513x^58+238x^59+76x^60+20x^61+11x^62+2x^64+3x^66

The gray image is a code over GF(2) with n=416, k=16 and d=184.
This code was found by Heurico 1.16 in 28.5 seconds.