The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+96x^22+292x^23+448x^24+1010x^25+1375x^26+4092x^27+1786x^28+4082x^29+1429x^30+1004x^31+371x^32+214x^33+105x^34+52x^35+18x^36+6x^37+3x^38

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 1.65 seconds.