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

generates a code of length 54 over Z16 who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+206x^52+188x^54+54x^56+24x^58+26x^60+12x^62+1x^64

The gray image is a code over GF(2) with n=432, k=9 and d=208.
This code was found by Heurico 1.16 in 0.316 seconds.