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

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

Homogenous weight enumerator: w(x)=1x^0+224x^46+60x^47+88x^48+332x^49+516x^50+632x^51+469x^52+632x^53+456x^54+332x^55+70x^56+60x^57+168x^58+10x^60+40x^62+4x^66+1x^68+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 19.3 seconds.