The generator matrix

 1  0  1  1  1  4  1  1  6  1  1  4 10  1  1  1  1  4  1  6  1  1  1 14  8  1  8  1  1  1 14  1  4  1  1 14  1  4  1  1  2  1  1  1  1  4  6 12 14  1  1  1  1
 0  1  1  0  3  1  5  4  1  8  3  1  1 10 15  2 13  1 11  1  2 13 14  1  1 11  1  9  9  6  1  0  4  6  3  1  0  1 15 10 10  4  5 10  5  1  1  2  1 13 12 12  0
 0  0  2  0  0  0  2 10  6  2  8 14  0  8  2 10  4  2 14 12  2  4 12 14 12  4 14 14 12 10  2  4  2  8 12 10 12 12  4 12 14  8  8  6  2 10  8  4  4  2 14 12  8
 0  0  0  2  0  2  2  8 14 14  6  4  6 14 10  6  2  6  8 12  0  8  0 12 14  6 14  6  4 14  4  2  4  8 12  0  0  0  8  6  8 12  6  6  2 14  4 10 12 12  8 12  8
 0  0  0  0  8  0  0  8  8  8  8  8  0  0  0  8  8  8  0  0  0  0  8  8  8  0  0  8  0  0  0  8  8  8  8  0  0  8  0  8  8  8  0  8  8  0  8  0  0  0  0  0  0
 0  0  0  0  0  8  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  0  8  0  8  0  8  0  0  0  0  8  8  8  8  8  0  0  8  0  0  0  8  0  8  8  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+68x^45+404x^46+804x^47+1637x^48+2948x^49+4868x^50+7676x^51+8823x^52+10712x^53+9394x^54+7936x^55+4721x^56+2788x^57+1400x^58+716x^59+343x^60+124x^61+86x^62+20x^63+57x^64+8x^66+2x^68

The gray image is a code over GF(2) with n=424, k=16 and d=180.
This code was found by Heurico 1.16 in 37.2 seconds.