The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+108x^52+322x^53+364x^54+602x^55+460x^56+610x^57+474x^58+466x^59+242x^60+166x^61+60x^62+110x^63+63x^64+22x^65+13x^66+6x^67+6x^68+1x^82

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 0.415 seconds.