The generator matrix

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

generates a code of length 20 over Z16 who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+122x^12+322x^14+64x^15+1217x^16+576x^17+5560x^18+1408x^19+14209x^20+1408x^21+5580x^22+576x^23+1238x^24+64x^25+312x^26+100x^28+2x^30+8x^32+1x^36

The gray image is a code over GF(2) with n=160, k=15 and d=48.
This code was found by Heurico 1.16 in 2.5 seconds.