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  1  1  1  1  1  1  1  1  2  2  1  2  1  4  2  1  1  2  1  4  2  1  4  2  2  2  1  1  2
 0 12  0  0  0  0  0  0  0  0  4 12 12  8  4  4  8  4  0  4  0  4 12  4  8  4 12 12 12  0  0 12  8  8  4  8  4  4 12 12  8  8  0  0 12 12 12 12  8  0  0  8 12
 0  0 12  0  0  0  4 12 12  8  4  4  8  4  4  0  8 12  8  4  0  8  4  8 12  8  8  4 12 12 12  0  0  8  0  0 12 12  8  4  8  0  4  8  8  8  4  8  8  4 12 12 12
 0  0  0 12  0  4  4  4  0  8  0  0  0  0  4 12  4  8  0  8 12  4  4  0 12  4 12  4  4  0 12  8  4 12  8 12  8  8 12  0  8 12 12  4  4 12  8  8  8 12 12  4  4
 0  0  0  0 12  4  8  4  4  0  8  4 12 12  4  8  8  4 12  0  4 12  4  8 12  4  8  0  8  0  8  4  0  0  0 12 12  8 12 12  8  8 12  0 12  4  4  8  4  8 12  8  0
 0  0  0  0  0  8  8  0  8  8  0  0  0  0  0  8  8  8  8  8  0  8  8  8  8  0  0  0  8  8  0  8  8  8  8  8  0  0  8  8  0  8  0  0  8  0  8  8  0  8  0  8  0

generates a code of length 53 over Z16 who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+70x^45+116x^46+162x^47+237x^48+202x^49+346x^50+762x^51+1392x^52+1738x^53+1322x^54+748x^55+380x^56+188x^57+156x^58+132x^59+82x^60+70x^61+38x^62+18x^63+17x^64+2x^65+6x^66+2x^67+2x^68+2x^69+1x^80

The gray image is a code over GF(2) with n=424, k=13 and d=180.
This code was found by Heurico 1.16 in 1.53 seconds.