The generator matrix

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

generates a code of length 19 over Z16 who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+336x^14+624x^15+1708x^16+3164x^17+6618x^18+7712x^19+6741x^20+3352x^21+1708x^22+464x^23+251x^24+44x^25+42x^26+3x^28

The gray image is a code over GF(2) with n=152, k=15 and d=56.
This code was found by Heurico 1.16 in 36.9 seconds.