The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+55x^22+332x^23+773x^24+1828x^25+3627x^26+6502x^27+6509x^28+6664x^29+3573x^30+1762x^31+702x^32+276x^33+105x^34+42x^35+15x^36+2x^39

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 4.06 seconds.