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  2  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  4  1  2  2  1  2
 0  2 12  6  0  6 12 10  6  0 10 12 10  0 14 12  8  6  4 10  0  6 12 10  8  6 12  2  0 14  4  2  4  0  4  6  6 10 10  8  4  6  2 12 12  6 14  0  8  2 14 12  2  6  6 10  0
 0  0  8  0  0  0  8  0  8  0  8  0  8  0  8  0  0  0  8  0  8  8  8  0  8  0  8  8  0  8  8  8  0  8  8  8  8  8  8  8  8  0  0  0  0  0  0  0  0  8  8  0  8  0  8  0  8
 0  0  0  8  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  8  0  8  8  0  8  8  0  0  8  8  0  8  8  8  8  0  0  8  0  8  0  8  0  8  0  8  8  0  0  0  0  0  8  8
 0  0  0  0  8  0  8  8  8  0  0  8  8  8  8  0  0  0  8  8  0  0  8  8  0  8  8  8  8  0  0  0  8  8  0  0  8  0  0  8  0  0  0  0  8  8  8  8  0  0  0  8  0  0  8  0  8
 0  0  0  0  0  8  0  8  8  8  8  8  0  8  0  8  0  8  0  8  0  8  8  0  8  0  8  8  0  0  8  0  0  0  8  0  8  8  0  8  0  0  0  0  0  8  8  8  8  8  8  0  0  0  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+103x^52+224x^54+448x^56+512x^57+470x^58+167x^60+100x^62+14x^64+6x^66+2x^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 0.197 seconds.