The generator matrix

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

generates a code of length 21 over Z16 who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+148x^12+92x^14+754x^16+256x^17+992x^18+1024x^19+8424x^20+9728x^21+7736x^22+1024x^23+1592x^24+256x^25+384x^26+292x^28+12x^30+53x^32

The gray image is a code over GF(2) with n=168, k=15 and d=48.
This code was found by Heurico 1.16 in 2.8 seconds.