The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 12  4  2  8  1  1  2  1  0  2 12  1  8  2  2  1  2  1  0  2  1  1  1  2  2  1  2  0  0  1
 0  2  0  0  0  2 14  2  4 12 14 10 12 14 12 14  4 14  0  4  2 10  2  4  0 12  2  0 14  2  2  8  2  4  2  6  8  0 14  6  4  2  0  8  4 10  4  6 12  2  2  0
 0  0  2  0  2  2 10  8  0  0  2 10  6  4 14  4  8  8  4  2 14 10  4  2  4  0  4  2 14 12  4 10  8  0  6  0 14 10 10  0  2 10 14  0 10  8  4  0  2 10  6  0
 0  0  0  2  2  8  2  6 14  4  4 14 14 10 12  4 10 14 12  6 12  6 14  0 10  2  2 12 12  4 10  8  0  2  6  6 10 12 12  0  4 14  4  2 12  6  2 12 12  2  0  0
 0  0  0  0  4  0  4 12 12 12 12  8  8  0 12 12 12  0  0  4  0 12 12  0 12  8  8  4  8  4  0  4  8  8  8  8 12  8  8  8  0  4  4 12  4  4  0  0  0  0  0  8

generates a code of length 52 over Z16 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+100x^44+318x^45+609x^46+1084x^47+1754x^48+2574x^49+3394x^50+4276x^51+4650x^52+4298x^53+3487x^54+2488x^55+1716x^56+932x^57+507x^58+286x^59+126x^60+100x^61+32x^62+24x^63+5x^64+2x^65+3x^66+2x^67

The gray image is a code over GF(2) with n=416, k=15 and d=176.
This code was found by Heurico 1.16 in 13.9 seconds.