The generator matrix

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

generates a code of length 52 over Z16 who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+516x^49+808x^50+754x^51+526x^52+490x^53+357x^54+284x^55+120x^56+94x^57+74x^58+70x^59+1x^66+1x^68

The gray image is a code over GF(2) with n=416, k=12 and d=196.
This code was found by Heurico 1.16 in 32.7 seconds.