The generator matrix

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

generates a code of length 53 over Z16 who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+34x^52+72x^53+4x^54+6x^55+1x^56+4x^58+4x^60+2x^63

The gray image is a code over GF(2) with n=424, k=7 and d=208.
This code was found by Heurico 1.16 in 0.0665 seconds.