The generator matrix

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

generates a code of length 21 over Z16 who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+41x^14+409x^16+288x^17+1656x^18+2432x^19+7152x^20+8896x^21+6975x^22+2432x^23+1838x^24+288x^25+280x^26+72x^28+7x^30+1x^38

The gray image is a code over GF(2) with n=168, k=15 and d=56.
This code was found by Heurico 1.16 in 2.2 seconds.