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

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

Homogenous weight enumerator: w(x)=1x^0+58x^45+370x^46+728x^47+1072x^48+1882x^49+2396x^50+3226x^51+4411x^52+4618x^53+4299x^54+3416x^55+2456x^56+1664x^57+983x^58+580x^59+305x^60+154x^61+71x^62+48x^63+10x^64+6x^65+9x^66+2x^67+2x^69+1x^72

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 14 seconds.