The generator matrix

 1  1  1  1  1  1  1  1  2  1  8  1  1  2  0  1  2  2  1  1  1  1  2  8  2  0  2  1
 0  2  0 14  4  6 12  2  6  2  2  4  6 14  2 10 10  2  8 10 14  2 14  2  6  2  0  0
 0  0 12  4  4  0  0  4  0 12  4  4  8  4  0  0  8  4  4  0 12  4 12 12  8  0  0  0
 0  0  0  8  0  0  0  0  0  8  8  0  0  8  0  8  0  8  0  8  0  8  0  8  8  0  0  0
 0  0  0  0  8  0  0  0  0  0  8  8  0  8  0  0  8  0  8  8  0  8  0  0  8  8  8  0
 0  0  0  0  0  8  0  0  0  0  0  0  8  8  8  0  8  8  0  8  0  8  8  0  8  0  8  0
 0  0  0  0  0  0  8  0  8  8  0  8  8  0  0  0  8  0  8  0  0  0  8  0  8  8  8  0
 0  0  0  0  0  0  0  8  8  0  0  0  0  0  8  8  8  0  8  8  0  8  8  8  8  8  0  0

generates a code of length 28 over Z16 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+36x^20+42x^21+108x^22+244x^23+483x^24+922x^25+2197x^26+1858x^27+4596x^28+1878x^29+2200x^30+930x^31+477x^32+222x^33+98x^34+38x^35+32x^36+8x^37+4x^38+2x^39+7x^40+1x^42

The gray image is a code over GF(2) with n=224, k=14 and d=80.
This code was found by Heurico 1.16 in 1.55 seconds.