The generator matrix

 1  0  0  1  1  1  4 12  1  1  8  1  1 10  8  1  6  1 10  1  2  4  1  1  4  1  1  1  1 10  2  6  0  4  1  1  8  1  1 12  1  1  1  1 12 10  1 12  6  1  1  1
 0  1  0  0 13 11  1  1  7  1  1 14 10  8  1 13  0  4  1 11  1  1 12 13  2 12  3  8  6 10  1  1  2  1 10  3  0  2 14  1 13 10  1 12  2  1  9  0  1  3  7  4
 0  0  1  1 13  4  7  4  5  0  5  6 15  1  6 11  1  8  7  2  0  7 15  6  1 10 15  7  1  1 11 14  1 13  1  6  1  0  0 10  9  5  2  9 14  5  1  1  1 12  9  0
 0  0  0  2 10  0  8 10  4 14  6 10  0 14  0 12  8  6  4  6 10 14  0  4  2  4 10 14  6 10  2  0  8 12  0  2 14  6  4 14 10  8 12  4 14 14  0 10  2 10  6  2
 0  0  0  0  8  8  8  8  8  8  8  0  0  0  8  8  0  0  0  0  0  0  8  0  8  8  0  8  8  0  0  0  8  0  8  0  0  8  0  8  0  0  8  0  8  8  0  8  0  8  8  0

generates a code of length 52 over Z16 who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+124x^45+748x^46+1466x^47+3421x^48+5032x^49+8111x^50+8502x^51+10884x^52+8714x^53+8067x^54+4770x^55+3316x^56+1296x^57+625x^58+252x^59+136x^60+30x^61+15x^62+16x^63+2x^64+4x^65+2x^67+2x^70

The gray image is a code over GF(2) with n=416, k=16 and d=180.
This code was found by Heurico 1.16 in 29.3 seconds.