The generator matrix

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

generates a code of length 56 over Z16 who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+176x^51+489x^52+832x^53+1059x^54+1150x^55+1068x^56+1216x^57+828x^58+578x^59+391x^60+180x^61+89x^62+78x^63+34x^64+12x^65+7x^66+2x^67+1x^72+1x^74

The gray image is a code over GF(2) with n=448, k=13 and d=204.
This code was found by Heurico 1.16 in 1.94 seconds.