The generator matrix

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

generates a code of length 54 over Z16 who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+142x^49+408x^50+948x^51+905x^52+1448x^53+970x^54+1188x^55+742x^56+748x^57+336x^58+180x^59+65x^60+54x^61+18x^62+16x^63+5x^64+6x^65+4x^66+4x^67+2x^69+2x^72

The gray image is a code over GF(2) with n=432, k=13 and d=196.
This code was found by Heurico 1.16 in 0.748 seconds.