The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+44x^13+139x^14+210x^15+337x^16+544x^17+958x^18+1840x^19+6712x^20+11112x^21+6808x^22+1844x^23+986x^24+544x^25+330x^26+192x^27+88x^28+44x^29+21x^30+10x^31+4x^32

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 4.06 seconds.