The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+80x^52+312x^53+284x^54+480x^55+604x^56+592x^57+584x^58+480x^59+295x^60+312x^61+60x^62+4x^64+5x^68+2x^72+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 0.262 seconds.