The generator matrix

 1  0  1  1  1 14  1  4  1 10  1  1  2  1  1  1  1  6  1  4  1  1  4  1  1  1  1  2  1  1  0  2  4  2  1  1  1  1  1  1  2  2 12  0  1  0  1  1  8  1  4  1
 0  1  1  0  7  1  2  1 11  1  5 14  1  3 14  3 12  1  2  1  5 12  1  8 13  6  9  1 14 11  1  1  1  1 15  5  6  4  9  3  4  6  1  2  0  4  8  8  1 13  2  1
 0  0  2  6  2  4 14  2  0  6  4  0 12 12  6  6  0 14  8  4  6 10  6  0 12 12 10  8  2  4 14  6  0  8  2  0  0 10  8  2 10 10  2  2  8  2 12  2  2  6  6 10
 0  0  0 12  0  0 12  8 12  0 12  4  0 12  4  0  0  8 12  8  0  4 12 12  8 12 12 12  8  0  8 12 12  4 12  0  8  0  0  4  8  4  4  8 12 12 12  8 12  4  0  0
 0  0  0  0  8  0  8  8  0  0  8  0  8  0  8  8  8  8  8  8  0  0  0  8  8  0  8  0  0  0  0  0  8  0  0  0  0  8  8  8  0  0  0  8  8  0  8  0  8  0  8  8
 0  0  0  0  0  8  0  0  0  0  0  8  0  8  8  8  8  8  0  8  8  8  0  8  0  0  0  8  8  0  8  0  0  0  8  8  8  8  8  0  8  0  8  8  0  8  8  0  8  0  8  0

generates a code of length 52 over Z16 who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+144x^45+383x^46+948x^47+1423x^48+2886x^49+3214x^50+5222x^51+4401x^52+5370x^53+3226x^54+2846x^55+1231x^56+782x^57+320x^58+178x^59+107x^60+30x^61+23x^62+22x^63+5x^64+4x^65+2x^66

The gray image is a code over GF(2) with n=416, k=15 and d=180.
This code was found by Heurico 1.16 in 27 seconds.