The generator matrix

 1  1  1  1  1  1  1  1  2  0  1  1  2  1  1  1 12  1  2  0  1  1  1  1  2  2  1  1
 0  2 12  6  0  6 12 10  6  2  0 10 10 12  6  0  2  6  6  2 10 10  6 12  6  6  0  0
 0  0  8  0  0  0  0  0  0  0  8  0  8  8  0  8  0  0  8  0  8  0  8  8  0  8  0  0
 0  0  0  8  0  0  0  0  0  0  0  8  8  8  8  0  8  8  0  0  8  0  8  8  0  0  0  0
 0  0  0  0  8  0  0  0  0  8  8  0  0  8  8  0  8  0  8  8  0  0  8  8  0  0  0  0
 0  0  0  0  0  8  0  0  8  8  0  0  8  0  8  0  8  8  8  0  0  0  0  8  8  0  0  0
 0  0  0  0  0  0  8  0  8  8  0  0  8  8  0  8  0  8  0  8  8  8  0  8  0  8  0  0
 0  0  0  0  0  0  0  8  8  0  0  8  0  8  8  8  0  8  8  0  8  8  8  8  8  8  0  0

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

Homogenous weight enumerator: w(x)=1x^0+43x^20+76x^22+48x^23+368x^24+304x^25+884x^26+1696x^27+1364x^28+1696x^29+884x^30+304x^31+351x^32+48x^33+76x^34+39x^36+8x^40+2x^44

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 0.378 seconds.