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  8  2  2  4  8 12  1  2  1  1  1  1  2  8  1  1  4  1 12  8  1  2  1  2  2  0  2  1
 0  2  0  0  0  2  6 14  0  8  0  0  6 10  6 12 14  8  2  4 10 10 10 12  2  4  2  4  2  4  4  0  4  0 14  2  8  2 10  6  2  8  2  2 10  8 12  2  6  8  8  8
 0  0  2  0  2  2  2  0  4 14  8 14 10  8 14  2 12 12 10  6  8  2  8  4 12 10  8  0  6 12  2  0 12 10  2  4  2  6  0 14  8 12  2  0  0 14  0  6 14  2  2  8
 0  0  0  2  2  0  2 10  8  2 14  4  4  2 14  6  0 10  2  8  6  4  0 12  8 12 10  2  2  2  2  6  6 12  0  8  8  0  6  6  4  6  0 12  6  8 12 14 10  8 14  0
 0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  0  0  8  8  8  0  8  8  8  8  0  0  8  8  8  8  8  8  0  0  0  8  0  0  0  8  8  0
 0  0  0  0  0  8  0  8  8  8  8  8  0  0  8  0  0  0  8  8  0  0  8  0  0  0  0  8  8  8  8  0  8  0  8  8  8  8  8  0  0  8  0  8  0  0  0  0  8  0  0  0

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

Homogenous weight enumerator: w(x)=1x^0+86x^44+278x^45+706x^46+1036x^47+1743x^48+2114x^49+3678x^50+4246x^51+5068x^52+4304x^53+3605x^54+2208x^55+1774x^56+826x^57+558x^58+266x^59+150x^60+62x^61+22x^62+16x^63+10x^64+4x^66+4x^67+3x^70

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 13.7 seconds.