The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+141x^50+328x^51+691x^52+744x^53+1461x^54+1672x^55+2091x^56+2336x^57+2121x^58+1580x^59+1392x^60+640x^61+581x^62+272x^63+160x^64+80x^65+46x^66+20x^67+13x^68+8x^69+2x^70+3x^72+1x^80

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 4.17 seconds.