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

generates a code of length 57 over Z16 who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+158x^52+224x^53+420x^54+396x^55+628x^56+640x^57+560x^58+344x^59+369x^60+116x^61+92x^62+28x^63+54x^64+40x^65+16x^66+5x^68+4x^69+1x^88

The gray image is a code over GF(2) with n=456, k=12 and d=208.
This code was found by Heurico 1.16 in 0.437 seconds.