The generator matrix

 1  0  1  1  1  6  1 12  1  1  1 14  8  1  2  1  1  1  1  8  0  1  1  1  1  1  4  1
 0  1 11  6 13  1  8  1 11 13  6  1  1  7  1  1  0 14  3  1  1  5 13 12  2 15  4  8
 0  0 12  0  4  0  0  8  8  0  0  4  4  8 12  4  4  4 12  8 12  0  4  4 12  0  4  0
 0  0  0 12  0  0  4  8 12  4  8  0  8  4  0  0  4  0 12  4  4  0  8 12  8  0  8  4
 0  0  0  0  8  0  8  8  8  0  0  0  0  0  8  8  8  0  0  0  8  8  0  8  8  8  8  0
 0  0  0  0  0  8  0  8  0  0  8  8  0  8  8  8  0  0  0  0  8  0  8  8  0  8  0  0

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

Homogenous weight enumerator: w(x)=1x^0+50x^22+114x^23+450x^24+802x^25+2122x^26+2954x^27+3474x^28+2898x^29+2122x^30+806x^31+413x^32+70x^33+54x^34+30x^35+14x^36+6x^37+4x^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 1.19 seconds.