The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+68x^14+154x^15+327x^16+818x^17+1777x^18+3790x^19+5992x^20+6826x^21+6044x^22+3866x^23+1818x^24+790x^25+294x^26+122x^27+48x^28+14x^29+8x^30+4x^31+6x^32+1x^34

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 3.6 seconds.