The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+184x^44+272x^45+868x^46+1348x^47+3065x^48+4656x^49+7502x^50+9512x^51+10605x^52+9680x^53+7648x^54+4808x^55+2885x^56+1168x^57+714x^58+264x^59+215x^60+32x^61+64x^62+4x^63+33x^64+4x^66+4x^68

The gray image is a code over GF(2) with n=416, k=16 and d=176.
This code was found by Heurico 1.16 in 38 seconds.