The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  1  2  1  2  1  1  2  1  2  2  1  1  2  1  2  2  2  2  2  2  1  1  1  1  1  1  1  1  2  2  1  1  1  1  2  2
 0 12  0 12  0 12  0 12  8  4  8  4  8  4  8  4 12 12  0 12 12 12  0  0  8  0  8  8  4 12  0  4  4  4  4  4  0  0  8 12  8 12  8  4  8  4  0  8  0 12  0 12  0  8
 0  0  8  0  0  8  8  8  8  8  8  8  0  0  0  0  0  0  0  8  8  8  0  8  8  8  8  0  8  0  8  0  8  8  0  0  0  8  8  0  8  8  0  8  0  0  0  0  0  0  0  8  8  8
 0  0  0  8  8  8  8  0  0  0  8  8  8  8  0  0  0  8  0  8  0  0  8  8  0  0  8  8  8  0  0  8  0  8  8  0  8  8  0  8  8  8  8  0  0  0  0  0  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+22x^52+212x^54+14x^56+4x^58+3x^72

The gray image is a code over GF(2) with n=432, k=8 and d=208.
This code was found by Heurico 1.16 in 0.0973 seconds.