The generator matrix

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

generates a code of length 55 over Z16 who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+646x^52+660x^53+742x^54+532x^55+546x^56+312x^57+250x^58+132x^59+154x^60+28x^61+88x^62+4x^64+1x^72

The gray image is a code over GF(2) with n=440, k=12 and d=208.
This code was found by Heurico 1.16 in 71.6 seconds.