The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+74x^45+175x^46+330x^47+911x^48+1552x^49+2463x^50+3544x^51+4582x^52+5410x^53+4852x^54+3632x^55+2401x^56+1406x^57+769x^58+324x^59+147x^60+60x^61+46x^62+38x^63+19x^64+10x^65+12x^66+4x^67+3x^68+3x^70

The gray image is a code over GF(2) with n=424, k=15 and d=180.
This code was found by Heurico 1.16 in 11.6 seconds.