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  8  0  2  2  2  2  0  1  1  2  1  4  4  1  1 12  1  1  2  8  1  2  1  8  2  2  1 12  1
 0  2  0  2  0  0  2 10  8  0  6  6  4  2  2 12 12 14  4  0  6  8 10  8  2  2 14 14  8  4 14  4 14  2  2  2 10  8  2 14  8 14  4 10  4  0  2  6 12 14  4  8
 0  0  2  2  0  6 10  8  6  4  6 12 12 12 14  2 12 14  6 12  4 10  6  2 12  6 10 12 14  2 10  6 14 12  6  0  6  8 14  4  0  4  2  8  6  4  8  0 10  0  2  6
 0  0  0  4  0  0  4  0  0  0 12  0  0  0  4  8  0  4  0  8  8  8  4  8 12  0  8  8  4 12  8 12 12  4 12  8  0 12  0 12 12  8  4  4  0  4  4  8 12  4  0  8
 0  0  0  0 12  0 12  4  4  4 12  4  8  0  8 12 12  8 12  8  0  4 12  4  0 12  8  0 12  0  4  8  4  4  0 12  4  8  0 12  8  8 12  0  0  4  4  8  4  4  4  4
 0  0  0  0  0  8  0  0  8  8  8  8  8  8  8  0  0  0  8  8  0  0  0  8  0  8  8  8  8  0  0  0  8  8  8  8  8  8  8  8  0  0  0  0  8  0  8  0  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+193x^44+216x^45+746x^46+904x^47+1692x^48+2272x^49+3650x^50+4164x^51+4979x^52+4456x^53+3636x^54+2320x^55+1561x^56+836x^57+642x^58+164x^59+210x^60+24x^61+54x^62+34x^64+4x^65+8x^66+2x^68

The gray image is a code over GF(2) with n=416, k=15 and d=176.
This code was found by Heurico 1.16 in 15.2 seconds.