The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+190x^45+658x^46+1542x^47+3214x^48+5104x^49+7506x^50+9100x^51+10830x^52+9076x^53+8104x^54+5110x^55+2770x^56+1242x^57+580x^58+330x^59+106x^60+28x^61+14x^62+12x^63+7x^64+6x^65+2x^66+2x^67+2x^69

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 43 seconds.