The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+48x^45+121x^46+258x^47+485x^48+656x^49+837x^50+1162x^51+1275x^52+1088x^53+837x^54+572x^55+363x^56+196x^57+112x^58+68x^59+45x^60+24x^61+10x^62+18x^63+7x^64+4x^65+2x^66+2x^67+1x^74

The gray image is a code over GF(2) with n=416, k=13 and d=180.
This code was found by Heurico 1.16 in 1.2 seconds.