The generator matrix

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

generates a code of length 52 over Z16 who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+28x^51+85x^52+7x^56+4x^59+3x^60

The gray image is a code over GF(2) with n=416, k=7 and d=204.
This code was found by Heurico 1.16 in 0.0523 seconds.