The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  2  4  0  1  1  1  2  1  2  1  4  2
 0 12  0  4  0  0  4 12  8 12  0  0 12  8  8  4  0  8  0 12  0 12 12 12 12  4  4  0
 0  0 12  4  0 12  4  8  4  4  0  0  0  4  4 12 12  4  4 12  8  0  8  8  8  0  4  0
 0  0  0  8  0  0  0  0  0  8  8  0  8  8  8  8  8  0  8  0  0  8  8  8  8  0  0  0
 0  0  0  0  8  0  0  8  8  8  8  0  0  8  0  0  0  8  8  0  8  0  0  8  8  0  0  8
 0  0  0  0  0  8  0  0  8  0  8  8  0  0  8  8  0  8  8  0  8  8  0  0  8  8  0  8
 0  0  0  0  0  0  8  0  0  0  8  0  8  8  8  0  8  8  0  0  8  0  8  0  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+81x^22+8x^23+193x^24+72x^25+562x^26+688x^27+905x^28+688x^29+560x^30+72x^31+165x^32+8x^33+70x^34+14x^36+7x^38+1x^40+1x^44

The gray image is a code over GF(2) with n=224, k=12 and d=88.
This code was found by Heurico 1.16 in 0.169 seconds.