The generator matrix

 1  1  1  1  1  1  1  1  1  2  1  2  4  1  0  1  1  1  1  1  1
 0 12  0 12  0 12  0 12  0 12  4 12 12 12  4 12  0  0 12 12  4
 0  0  8  0  0  0  0  0  0  0  0  8  0  0  8  8  8  8  0  8  0
 0  0  0  8  0  0  0  0  0  0  0  0  0  8  8  8  0  0  8  8  8
 0  0  0  0  8  0  0  0  0  0  0  8  8  8  0  8  8  0  8  8  0
 0  0  0  0  0  8  0  0  0  8  8  0  8  8  0  8  0  8  0  8  8
 0  0  0  0  0  0  8  0  0  8  0  8  0  8  8  0  0  8  0  0  8
 0  0  0  0  0  0  0  8  0  8  8  8  0  0  8  8  8  0  8  0  0
 0  0  0  0  0  0  0  0  8  8  0  8  8  0  0  0  8  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+51x^14+48x^15+125x^16+32x^17+117x^18+848x^19+2221x^20+1216x^21+2318x^22+848x^23+174x^24+32x^25+58x^26+48x^27+34x^28+15x^30+4x^32+1x^34+1x^36

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 5.47 seconds.