The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  0  1  1  2  1  1  1  1  2  1  1  1  2  1  1  2  1 12  1  2  1  1  1  1  8  1  1  1  1  2  0 12  1  1  1  0 12  1
 0  2  0  6  4  6 12  2  8  0  6  6  4  4  2 10 14  2  6  2  8  4 10 12  6 10  0 14  0  4  2  2  8 12  6 10  2 10 14  6  4 14 12  2  8  0 14  8  2  2  2 10  2 12  2  2  2
 0  0 12  0  4  0  0  0  8  4  4 12  8 12  4 12  0  8  0  4  4  4  8  0 12 12 12  8  8  0  4  8  8 12 12  8 12  4  4  4  8  0  0  0 12 12  4  4 12  4  0  0  4  8  8  0  4
 0  0  0 12  0  0  8 12 12 12  4  0  4 12  8 12 12 12  8  4  8  8  0  0  4 12  4 12  4  4 12  4 12  8  4  0  4  0  0  0  0  8  4 12 12 12  8  8  0 12  0 12  4 12  0  8  4
 0  0  0  0  8  0  8  8  0  0  0  8  8  8  8  0  8  0  0  0  8  0  8  8  8  8  0  0  8  0  0  0  8  8  8  8  8  0  0  8  0  8  8  8  8  8  8  8  8  8  8  0  8  0  8  8  8
 0  0  0  0  0  8  0  0  0  0  0  0  0  0  8  8  8  8  0  8  8  8  8  8  0  8  8  0  0  8  0  8  8  8  8  0  0  0  0  0  0  0  8  8  0  8  8  0  8  8  8  0  0  8  0  0  8

generates a code of length 57 over Z16 who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+71x^50+138x^51+263x^52+418x^53+599x^54+858x^55+1137x^56+1310x^57+1149x^58+872x^59+552x^60+354x^61+229x^62+98x^63+49x^64+20x^65+20x^66+18x^67+13x^68+8x^69+11x^70+1x^72+2x^73+1x^86

The gray image is a code over GF(2) with n=456, k=13 and d=200.
This code was found by Heurico 1.16 in 1.37 seconds.