The generator matrix

 1  1  1  1  1  1  1  1  2  2  2  1  2  1  4  1  1  2  0  2  1
 0  2  0  2  0 10 12  6  2  6  4  6 14  4  2  0 14  6  0  2  4
 0  0  2  2 12 14  6  0  2  0  2  6  4  2  2  6  4  0  2  2  2
 0  0  0  8  0  0  0  0  0  8  0  8  8  0  0  8  8  0  8  8  0
 0  0  0  0  8  0  0  0  0  8  8  8  0  8  8  0  0  8  8  8  0
 0  0  0  0  0  8  0  0  8  0  8  0  0  8  8  0  8  8  8  8  8
 0  0  0  0  0  0  8  0  8  0  0  0  8  8  0  8  8  8  8  0  0
 0  0  0  0  0  0  0  8  8  8  0  0  8  0  8  0  8  0  8  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+74x^15+328x^16+702x^17+1615x^18+3778x^19+5150x^20+9350x^21+5228x^22+3742x^23+1642x^24+698x^25+280x^26+86x^27+42x^28+2x^29+3x^30+5x^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 2.88 seconds.