The generator matrix

 1  0  1  1  1  4  1  1  0  1  6  1  1  1 14  1  8  1  1  6  1  1 12  1  1  1 14  1  1  1  1  1  1  1  1 14  1  8  1  1  2 12  2  8  1  0 10  8  1  8  8  0  1
 0  1  1  0 11  1  1  0  1 10  1  5 15  2  1 15  1 10  4  1 14  3  1  7  1 12  1 12 15  9 10  0 11  8  1  1 12  1 10 15 12  2  2  2  6  1  1  0 12 12  8  2  8
 0  0  2  0  0  8 10  2  2  2  2  4  8  0  8  6 14 14 10  2  4 12  4 12 14 10  8  8 10  4  6 12  2 12 12  2 14  4 10 10  6  6 14  2  6  0  8  2  8  2  2  6  0
 0  0  0  2  0 10 14 14  6  8  0 14  6 14 14 12  4 14  8  2 12  6  6  8  2  8  8  6 10 10 14 10  8  4  0  6  2  0  6  4  6 12  4  0  4  8 10  2 12 14  4  6 12
 0  0  0  0 12  0  0 12 12  4  4 12  8  4 12 12  0  0  8  8  4 12  8  0  4  4  4  0  8  8  4 12 12 12  0  8  0 12  0  4  4  8  4 12 12  8  0  0  4 12  4  4  0

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

Homogenous weight enumerator: w(x)=1x^0+104x^45+365x^46+1206x^47+1739x^48+3158x^49+4826x^50+7384x^51+8939x^52+10286x^53+9014x^54+7096x^55+4901x^56+3374x^57+1488x^58+906x^59+369x^60+228x^61+77x^62+46x^63+19x^64+6x^66+2x^67+2x^69

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 37.1 seconds.