The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  0  1  1  1  6  1  1 10  1 12  1  1  1  6  1  1  1  1  1  0  1 12 10  1  1  1  1  6  1  1  1 10 10  1  1  1  1  2  1  1
 0  1  3  6  5  1 12 15  1 10  9  1  1  0  3  5  1  6 15  1  9  1 12 10  5  1  0  6 10 15 12  1  9  1  1  6 14  0  0  1 10 10  0  1  1  3  8 10  3 12 12 12
 0  0  8  0  0  0  0  0  0  8  0  0  0  8  8  8  8  8  8  8  8  8  0  8  0  8  8  0  0  0  8  0  0  8  8  8  8  8  8  8  0  0  8  0  0  0  8  0  0  8  8  8
 0  0  0  8  0  0  0  8  0  8  8  0  8  8  0  8  8  8  0  8  0  0  0  0  8  8  0  0  8  8  8  8  0  8  0  8  0  0  8  8  0  8  8  8  0  8  8  8  0  0  0  0
 0  0  0  0  8  0  0  0  8  0  8  0  8  0  0  8  0  0  8  8  0  8  0  0  0  0  0  8  8  8  0  0  8  0  8  8  8  8  8  8  0  0  8  0  8  8  8  8  8  8  0  8
 0  0  0  0  0  8  0  8  8  0  8  0  0  0  0  0  8  8  8  8  8  0  8  8  8  8  8  0  8  0  8  0  8  8  8  8  8  0  0  0  8  0  0  8  0  8  8  0  8  0  0  8
 0  0  0  0  0  0  8  8  0  8  8  8  8  0  8  8  0  0  0  8  8  0  8  0  0  8  8  8  8  0  0  0  0  0  8  8  8  0  8  8  8  8  0  8  0  8  0  0  0  0  8  0

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

Homogenous weight enumerator: w(x)=1x^0+92x^46+200x^47+287x^48+776x^49+662x^50+1696x^51+783x^52+1744x^53+610x^54+776x^55+306x^56+168x^57+33x^58+16x^59+26x^60+5x^62+1x^64+5x^66+2x^68+1x^70+1x^72+1x^76

The gray image is a code over GF(2) with n=416, k=13 and d=184.
This code was found by Heurico 1.16 in 3.9 seconds.