The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  8  1  1  4  2  1  1  2  1  1  1  1  1  1  1  0  1  1  1  1  1  2  1  8  1  1 12  1  1  2  0  2  1  1  1  2  1  1
 0  2  0  6  4 14 12  2  0  6 12 10  8 14 12  2  0 14 14  2 12 10  2  2 12  2  6  2  6  0  6 14 10  2  2 10  4  6  4  8 14  4  2  0  8  2 10  8 10  2  6  4  4  0  2 12 14
 0  0 12  0  4  4  0  4  0  8  0  8 12 12 12  4  8  8  4 12  8  8 12  4  8 12  8  0  0  0  0  8  0  0  0  4  4 12 12 12  4  8 12  4  0  8  4  0  0  8  8  4 12 12 12  4 12
 0  0  0  8  0  0  0  0  0  8  8  8  8  8  8  8  8  0  8  0  0  8  0  8  0  8  8  0  0  8  0  0  0  0  8  0  8  0  8  0  0  8  0  0  8  8  8  0  8  0  0  8  8  0  8  0  0
 0  0  0  0  8  0  0  8  8  8  8  0  8  0  0  8  0  8  8  0  8  8  0  8  8  8  0  8  0  0  8  0  0  8  8  8  0  0  8  8  0  8  8  0  0  8  0  0  8  8  8  0  8  0  0  0  8
 0  0  0  0  0  8  0  8  0  0  0  0  0  8  0  8  0  0  8  0  8  8  0  8  8  0  8  0  8  8  8  8  0  8  8  0  8  0  8  0  8  8  0  8  0  0  8  8  0  0  0  0  0  0  8  0  8
 0  0  0  0  0  0  8  0  0  0  8  8  0  8  0  8  0  8  8  0  8  8  8  0  0  8  0  0  8  8  0  0  8  8  8  8  8  0  0  8  8  8  8  8  8  8  0  8  0  8  0  8  8  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+114x^50+68x^51+316x^52+296x^53+690x^54+828x^55+1229x^56+1200x^57+1215x^58+828x^59+643x^60+296x^61+241x^62+68x^63+94x^64+33x^66+13x^68+9x^70+7x^72+2x^74+1x^88

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 1.41 seconds.