The generator matrix

 1  1  1  1  1  1  1  1  1  1  2  1  2  4  2  1  1  4  2  2  1
 0 12  0  0  0  0  0  0  8 12  4  4  4  8  8 12 12 12  4  8  0
 0  0 12  0  0  0  4 12 12  4 12  0  8  0  4 12 12  4 12  4  8
 0  0  0 12  0  4  4 12  0  0  8  4  4 12  0  4  4  8 12 12  8
 0  0  0  0 12  4  0 12  4  4  8  0  8  4  0  8  8  4  4  4  0
 0  0  0  0  0  8  0  0  0  0  0  0  0  0  8  8  8  8  8  8  0
 0  0  0  0  0  0  8  0  0  8  8  8  0  8  0  0  8  0  0  0  8
 0  0  0  0  0  0  0  8  8  8  0  8  8  0  0  0  0  0  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+46x^13+137x^14+228x^15+378x^16+600x^17+1197x^18+2812x^19+6456x^20+8944x^21+6498x^22+2916x^23+1248x^24+612x^25+338x^26+180x^27+104x^28+34x^29+21x^30+8x^31+5x^32+4x^33+1x^34

The gray image is a code over GF(2) with n=168, k=15 and d=52.
This code was found by Heurico 1.16 in 3.74 seconds.