The generator matrix

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

generates a code of length 21 over Z16 who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+20x^13+95x^14+32x^15+245x^16+448x^17+791x^18+1328x^19+2901x^20+4504x^21+3022x^22+1408x^23+886x^24+384x^25+166x^26+48x^27+58x^28+20x^29+19x^30+4x^32+3x^34+1x^36

The gray image is a code over GF(2) with n=168, k=14 and d=52.
This code was found by Heurico 1.16 in 3.19 seconds.