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  1  1  2  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  2  1  1  1  2  4  1  1  1  1  4  4
 0 12  0  0  0  4 12 12  8  8  0  0  4  4  4 12  0  8  4  4  8  8  4  4  8 12 12 12 12  4  0  8  0 12  0 12 12 12  0  0  0  4  4  0  8 12 12 12  4  8  8  4  4 12  0  8  8
 0  0 12  0  4  4  4  0  8  0  4 12  4  4  0  8  0  8 12  8 12 12 12  8  0  8  8  4 12  0  4 12  8  0  0  0  4  4  4  0 12  8 12 12  0 12 12  4  4  0 12  0  8  4  8  4  4
 0  0  0 12  4  8  4  4  0  4  4  0  0 12  4  8  0 12  4  4 12  8  0  0 12  0  8  8  4  4 12  0  8  8 12 12 12  8  8  8  8  8 12 12 12  4  0  4  8  0  4  0  8  0 12  8  8
 0  0  0  0  8  8  0  8  8  8  0  8  0  8  0  8  8  8  0  0  8  8  0  0  0  8  0  8  8  8  0  0  8  0  8  0  8  0  8  0  8  0  0  8  8  0  0  8  0  8  8  8  8  0  8  8  0

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

Homogenous weight enumerator: w(x)=1x^0+106x^52+4x^53+152x^54+112x^55+421x^56+536x^57+400x^58+112x^59+103x^60+4x^61+42x^62+22x^64+12x^66+14x^68+2x^70+4x^72+1x^100

The gray image is a code over GF(2) with n=456, k=11 and d=208.
This code was found by Heurico 1.16 in 4.41 seconds.