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

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

Homogenous weight enumerator: w(x)=1x^0+166x^45+284x^46+546x^47+868x^48+1258x^49+1807x^50+2166x^51+2357x^52+2206x^53+1765x^54+1128x^55+798x^56+486x^57+227x^58+184x^59+64x^60+36x^61+11x^62+6x^63+5x^64+8x^65+2x^66+2x^67+3x^68

The gray image is a code over GF(2) with n=416, k=14 and d=180.
This code was found by Heurico 1.16 in 4.56 seconds.