The generator matrix

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

generates a code of length 53 over Z16 who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+78x^49+520x^50+656x^51+806x^52+582x^53+450x^54+312x^55+295x^56+112x^57+169x^58+60x^59+24x^60+24x^61+5x^62+1x^64+1x^68

The gray image is a code over GF(2) with n=424, k=12 and d=196.
This code was found by Heurico 1.16 in 0.171 seconds.