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  1  2  1  1  1  1  1  2  1  2  1  1  2  1  1  1  8  1  1  2  2  4  2  2  1  1  2
 0 12  0  0  0  0  0  0  0  4 12 12  4 12  4 12  8 12  8 12  0  8 12  8 12  4 12  0  4 12  8 12 12 12  4  4  8  0 12 12  0  4  4 12 12  0  8  8  0 12  0  8
 0  0 12  0  0  8 12 12  4  4  4  8  4 12  0  8  0  8  0  4  4  4  4  4  8 12  0 12  0  0  0  8 12  0  8  0  8 12  0  4  4 12 12  8  8  0 12  0  8  4 12  8
 0  0  0 12  0 12 12  4  8  0  0  0  4 12  4  4  8 12  4  4  8  8  4  4  0  0  4  4  8 12  8  8  8  0  8  8 12 12  8  4  0  0  8 12  0  8  0 12 12 12  4  8
 0  0  0  0 12  4  8  4  4  0  4  4  4  0  8 12 12  8  8  4  8 12  0 12  8  4 12  0 12 12  4  0 12  4 12  0 12 12  4  8  0  0  0  0 12  4 12  8 12  0 12  8

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

Homogenous weight enumerator: w(x)=1x^0+218x^46+180x^48+588x^50+512x^51+1170x^52+512x^53+586x^54+112x^56+138x^58+30x^60+28x^62+10x^64+10x^66+1x^80

The gray image is a code over GF(2) with n=416, k=12 and d=184.
This code was found by Heurico 1.16 in 21 seconds.