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  2  2  2  1  2  2  2  1  8  1  2  1  1  1  2  2  1  2  1  2  1  1  1  1  2
 0 12  0  0  0  4 12  4  8  0  4  0  8  4  4  4  4  8  8  0  0 12  4  4 12 12  8  0  8  8  8  0  4  0  4  8  4 12  8  0  8 12 12 12  0  8  0 12 12 12 12 12 12
 0  0 12  0  4  4 12  0  0  4  8  0 12 12  8  4  4  0  8 12 12 12  0  4  0 12  0  8  4  4  8 12  0  4  4  8  4  4  8  4 12 12  4  4  4 12 12  8  4  0  4  0  0
 0  0  0 12  4  0 12  4  4  8  0  8  4  4  4  8  8  4  0  0  4 12  8  4  4 12  4  0  0  8 12  0 12  4  0  4  8  8 12  0  0  0  4  4  4  0  8  4  4  0  8  4  0
 0  0  0  0  8  0  0  8  0  8  8  0  0  0  0  8  0  0  0  0  8  8  8  0  8  8  8  8  8  0  8  0  0  8  8  0  0  0  8  8  8  8  0  8  0  8  8  0  0  0  8  0  0
 0  0  0  0  0  8  0  8  8  8  0  8  8  0  8  8  0  8  8  8  0  0  8  8  8  8  8  8  0  0  8  0  8  8  8  0  0  8  8  0  0  0  0  8  0  8  8  8  8  8  0  0  0
 0  0  0  0  0  0  8  0  8  8  8  0  0  0  0  0  0  0  8  8  8  0  8  0  8  8  0  0  0  8  8  8  0  0  8  8  8  8  0  0  8  8  8  0  0  0  0  8  0  8  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+66x^45+116x^46+166x^47+196x^48+264x^49+265x^50+326x^51+1507x^52+2476x^53+1480x^54+370x^55+250x^56+204x^57+138x^58+118x^59+74x^60+58x^61+44x^62+40x^63+16x^64+4x^65+5x^66+4x^67+3x^68+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 45 seconds.