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

generates a code of length 52 over Z16 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+43x^44+32x^45+71x^46+48x^47+129x^48+144x^49+437x^50+800x^51+724x^52+800x^53+428x^54+144x^55+96x^56+48x^57+64x^58+32x^59+25x^60+11x^62+6x^64+11x^66+1x^70+1x^86

The gray image is a code over GF(2) with n=416, k=12 and d=176.
This code was found by Heurico 1.16 in 0.458 seconds.