The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+128x^12+100x^14+858x^16+256x^17+1344x^18+4096x^19+3892x^20+11776x^21+3176x^22+4096x^23+1960x^24+256x^25+480x^26+296x^28+20x^30+29x^32+4x^36

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 4.51 seconds.