The generator matrix

 1  1  1  1  1  1  1  1  1  1  2  1  2  2  2  2  1  1  4  4  1
 0 12  0  0  0  4 12  4  0  8  4 12 12 12  8  4  0 12 12  0  4
 0  0 12  0  4  4 12  0  0  0  4  8  8 12 12  0  4 12  4 12  4
 0  0  0 12  4  0 12  4  0  4  8  0  0 12 12  4  4  8  4  0  0
 0  0  0  0  8  0  0  0  8  0  8  0  8  0  8  0  8  0  0  8  0
 0  0  0  0  0  8  0  0  8  8  8  8  8  8  8  0  0  8  0  8  0
 0  0  0  0  0  0  8  0  0  0  0  0  0  8  8  8  0  8  0  8  8
 0  0  0  0  0  0  0  8  8  8  0  8  0  8  0  8  8  0  0  8  0

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

Homogenous weight enumerator: w(x)=1x^0+94x^14+440x^16+64x^17+904x^18+1024x^19+3620x^20+3968x^21+3756x^22+1024x^23+976x^24+64x^25+344x^26+76x^28+22x^30+7x^32

The gray image is a code over GF(2) with n=168, k=14 and d=56.
This code was found by Heurico 1.16 in 15.6 seconds.