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

generates a code of length 71 over Z16 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+1x^72+24x^73+2x^74+4x^75

The gray image is a code over GF(2) with n=568, k=5 and d=288.
This code was found by Heurico 1.16 in 0.168 seconds.