The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+340x^45+1627x^46+3394x^47+6565x^48+10650x^49+14435x^50+18252x^51+20060x^52+18894x^53+15176x^54+10312x^55+5985x^56+3174x^57+1463x^58+430x^59+186x^60+78x^61+35x^62+10x^63+3x^64+2x^67

The gray image is a code over GF(2) with n=416, k=17 and d=180.
This code was found by Heurico 1.16 in 116 seconds.