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

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

Homogenous weight enumerator: w(x)=1x^0+38x^50+48x^51+175x^52+120x^53+331x^54+272x^55+864x^56+408x^57+884x^58+272x^59+329x^60+104x^61+146x^62+48x^63+27x^64+8x^65+6x^66+7x^68+3x^70+4x^72+1x^92

The gray image is a code over GF(2) with n=456, k=12 and d=200.
This code was found by Heurico 1.16 in 0.451 seconds.