The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  0  1  1  2  4  1 12  1  1  1  1
 0  2  0  0  0  2  6 14  8  8  8  4  2  2 12 14 10  2 14 14  6  2  4  4  2  2 14  0
 0  0  2  0  2  2 10  0 12 14  2  4 14 10  6  8 10  4  8  8  8 12 14  2 14  0  2  0
 0  0  0  2  2  8 10  2  4  0  6 14  2  4 14  2  4 12  4  6 14  0  0  4 12  8  2  0
 0  0  0  0  8  8  0  8  8  8  0  8  8  0  0  0  8  0  8  8  0  8  8  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+55x^22+290x^23+490x^24+980x^25+1571x^26+2734x^27+3981x^28+3010x^29+1579x^30+950x^31+411x^32+176x^33+90x^34+42x^35+13x^36+10x^37+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 1.53 seconds.