The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+299x^50+672x^51+2086x^52+2972x^53+5697x^54+6960x^55+9263x^56+9608x^57+9651x^58+6892x^59+5582x^60+2908x^61+1769x^62+632x^63+341x^64+64x^65+74x^66+12x^67+32x^68+14x^70+7x^72

The gray image is a code over GF(2) with n=456, k=16 and d=200.
This code was found by Heurico 1.16 in 62.6 seconds.