The generator matrix

 1  1  1  1  1  1  1  1  1  2  1  2  1  1  4  1  1  0  2  1  4  1  1  1  2  1  1  1
 0 12  0 12  0 12  0 12  0 12 12 12  0 12 12  4  0  4 12  8 12  0  0 12  8 12 12  0
 0  0  8  0  0  0  0  0  0  0  0  0  8  0  0  0  8  0  8  8  8  8  8  8  0  0  8  0
 0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  8  8  0  8  8  8  0  8  8  0  0  0
 0  0  0  0  8  0  0  0  0  0  0  0  8  8  8  8  0  0  8  8  8  0  8  0  0  8  8  8
 0  0  0  0  0  8  0  0  0  0  8  0  0  8  8  0  8  8  0  8  0  8  8  0  0  0  0  8
 0  0  0  0  0  0  8  0  0  0  8  0  0  0  8  8  8  0  8  0  8  8  8  0  8  0  0  0
 0  0  0  0  0  0  0  8  0  0  8  8  8  8  8  8  8  8  8  0  8  8  8  8  0  8  0  0
 0  0  0  0  0  0  0  0  8  0  8  8  8  0  0  8  8  0  0  8  8  0  8  8  8  8  8  0
 0  0  0  0  0  0  0  0  0  8  0  8  0  0  8  0  8  8  8  8  8  0  0  0  0  0  8  0

generates a code of length 28 over Z16 who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+27x^18+6x^19+98x^20+38x^21+158x^22+136x^23+235x^24+840x^25+1341x^26+4100x^27+2396x^28+4100x^29+1380x^30+840x^31+262x^32+136x^33+133x^34+38x^35+66x^36+6x^37+30x^38+13x^40+3x^42+1x^48

The gray image is a code over GF(2) with n=224, k=14 and d=72.
This code was found by Heurico 1.16 in 50.6 seconds.