The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  2  2  2  1  4  1  1  1  1  1
 0 12  0  0  0  4 12  4  8  0  4  0  8  0  4 12  4  8  0  8  0
 0  0 12  0  4  4 12  0  0  4  8  4  0 12 12  4 12  4  4  0  0
 0  0  0 12  4  0 12  4  4  8  0 12  4  0  4 12  8  4 12  4  0
 0  0  0  0  8  0  0  8  0  8  8  8  0  0  8  8  0  8  0  8  0
 0  0  0  0  0  8  0  8  8  8  0  0  0  8  8  8  0  8  8  8  0
 0  0  0  0  0  0  8  0  8  8  8  8  8  8  8  0  0  8  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+29x^14+48x^15+100x^16+126x^17+261x^18+424x^19+1643x^20+2934x^21+1669x^22+368x^23+279x^24+138x^25+85x^26+56x^27+25x^28+2x^29+2x^30+2x^34

The gray image is a code over GF(2) with n=168, k=13 and d=56.
This code was found by Heurico 1.16 in 0.278 seconds.