The generator matrix

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

generates a code of length 20 over Z16 who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+42x^14+46x^15+96x^16+120x^17+210x^18+846x^19+1350x^20+880x^21+226x^22+122x^23+78x^24+24x^25+30x^26+10x^27+10x^28+4x^30+1x^32

The gray image is a code over GF(2) with n=160, k=12 and d=56.
This code was found by Heurico 1.16 in 0.076 seconds.