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
 0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  0  0  8  8
 0  0  8  0  0  0  0  0  0  0  0  0  8  0  0  8  8  8  8  0  8  8  8  0  8  8  8  0
 0  0  0  8  0  0  0  0  0  0  0  0  8  8  8  8  8  0  8  8  0  8  0  0  0  8  0  0
 0  0  0  0  8  0  0  0  0  0  0  8  0  8  8  0  8  8  8  0  8  8  0  0  0  0  0  8
 0  0  0  0  0  8  0  0  0  0  0  8  0  0  8  8  8  8  0  0  0  8  0  8  8  8  8  8
 0  0  0  0  0  0  8  0  0  0  8  0  0  0  8  8  0  0  0  8  0  8  8  8  0  8  8  0
 0  0  0  0  0  0  0  8  0  0  8  0  0  8  0  0  8  0  0  0  8  8  8  0  0  8  8  8
 0  0  0  0  0  0  0  0  8  0  8  8  8  8  0  0  0  0  0  8  8  0  8  8  0  8  0  0
 0  0  0  0  0  0  0  0  0  8  8  8  8  0  0  8  8  8  0  0  8  0  0  8  0  0  8  0

generates a code of length 28 over Z16 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+148x^20+255x^24+7384x^28+255x^32+148x^36+1x^56

The gray image is a code over GF(2) with n=224, k=13 and d=80.
This code was found by Heurico 1.16 in 4.25 seconds.