The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+30x^14+58x^15+101x^16+162x^17+226x^18+490x^19+1679x^20+2690x^21+1710x^22+446x^23+240x^24+214x^25+70x^26+30x^27+24x^28+6x^29+12x^30+2x^32+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 0.321 seconds.