The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+99x^50+112x^51+484x^52+696x^53+1454x^54+1640x^55+2651x^56+2256x^57+2590x^58+1696x^59+1363x^60+632x^61+416x^62+136x^63+81x^64+35x^66+22x^68+10x^70+3x^72+4x^74+3x^76

The gray image is a code over GF(2) with n=456, k=14 and d=200.
This code was found by Heurico 1.16 in 3.29 seconds.