The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1 12  8  2  2  1  1  2  8  1  1  2  1  1  1  1
 0  2  0  2  0  8  6 14  0  0  2 14  8  2 12 12 14  0  6 12  2 10 14 12 14 14 12 12
 0  0  2  2  0  6 14  8  0  2 14  0 10  8  2  2  4 12  0 10  6  6  8 14  4 12 10  0
 0  0  0  4  0  0 12  0 12 12  8  4 12 12  4 12  8 12 12  0  0 12  8  4  4  4  4 12
 0  0  0  0 12  4  4  4 12  8 12  0 12  4  4  8  8  0  4  8  4  4  8  0  4  0  4  4

generates a code of length 28 over Z16 who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+102x^22+246x^23+458x^24+948x^25+1664x^26+2804x^27+3731x^28+3098x^29+1720x^30+896x^31+399x^32+160x^33+93x^34+36x^35+19x^36+2x^37+4x^38+2x^39+1x^42

The gray image is a code over GF(2) with n=224, k=14 and d=88.
This code was found by Heurico 1.16 in 1.69 seconds.