The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+45x^18+22x^19+156x^20+158x^21+298x^22+442x^23+460x^24+1754x^25+3731x^26+3756x^27+11034x^28+3740x^29+3812x^30+1828x^31+515x^32+452x^33+251x^34+94x^35+104x^36+38x^37+50x^38+2x^39+16x^40+2x^41+5x^42+2x^44

The gray image is a code over GF(2) with n=224, k=15 and d=72.
This code was found by Heurico 1.16 in 6.07 seconds.