The generator matrix

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

generates a code of length 28 over Z16 who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+181x^16+404x^20+1076x^24+1024x^26+27364x^28+1024x^30+1143x^32+380x^36+156x^40+12x^44+3x^48

The gray image is a code over GF(2) with n=224, k=15 and d=64.
This code was found by Heurico 1.16 in 4.8 seconds.