The generator matrix

 1  0  1  1  1 12  6  1  1  1  2  1  1  1  4  4  8  1  1  1  1  0 10  1  8  0 12  1
 0  1  1  4  3  1  1  6 13 10  1  7 11  8  1  1  1 12  5  3 15  0  1 12  1  1  1  3
 0  0  2  2  0  6  0  8  4  6 10  2  4  2  2  4 10  0  0  6  8  2  6  6  4  0 14  0
 0  0  0  8  0  0  0  0  0  8  0  0  0  8  8  8  8  8  0  0  8  8  0  8  8  0  8  8
 0  0  0  0  8  0  0  0  8  8  8  8  0  0  8  8  0  8  0  8  0  8  0  0  8  8  8  8
 0  0  0  0  0  8  0  0  0  0  8  0  0  0  8  0  8  0  8  8  8  8  0  8  8  8  0  8
 0  0  0  0  0  0  8  8  8  0  0  8  8  8  8  8  8  8  0  8  0  0  0  8  8  8  0  8

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

Homogenous weight enumerator: w(x)=1x^0+155x^22+208x^23+771x^24+1496x^25+4058x^26+5448x^27+8484x^28+5488x^29+4082x^30+1504x^31+697x^32+184x^33+148x^34+8x^35+28x^36+3x^38+3x^40+2x^42

The gray image is a code over GF(2) with n=224, k=15 and d=88.
This code was found by Heurico 1.16 in 13.2 seconds.