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

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

Homogenous weight enumerator: w(x)=1x^0+121x^44+8x^45+320x^46+44x^47+375x^48+232x^49+874x^50+1244x^51+1812x^52+1272x^53+876x^54+228x^55+354x^56+24x^57+176x^58+20x^59+122x^60+52x^62+30x^64+6x^66+1x^76

The gray image is a code over GF(2) with n=416, k=13 and d=176.
This code was found by Heurico 1.16 in 1.41 seconds.