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

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

Homogenous weight enumerator: w(x)=1x^0+149x^52+24x^54+160x^55+377x^56+704x^57+288x^58+160x^59+98x^60+8x^62+69x^64+9x^68+1x^104

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 1.07 seconds.