The generator matrix

 1  1  1  1  1  1  1  1  2  1  2  2  1  1  1  1  2  1  2  1
 0  2  0  2  0  0  2  6  2  8  4  6  6  0  4  2  8  0 12  8
 0  0  2  2  0  6  2  4  2 12  2  0 10  4  6  4 10  2  2  0
 0  0  0  4  0  0  0  0  0  0 12  4  8  4  4 12  8 12  8  0
 0  0  0  0 12  0  0  0 12  8 12 12 12  8  4  0  4  8  0  8
 0  0  0  0  0 12  8 12 12 12  0  8  0  8  4 12  0  0  4 12

generates a code of length 20 over Z16 who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+74x^13+173x^14+540x^15+1224x^16+2552x^17+6554x^18+10114x^19+22926x^20+10188x^21+6744x^22+2586x^23+1110x^24+488x^25+158x^26+70x^27+18x^28+10x^29+3x^30+2x^31+1x^32

The gray image is a code over GF(2) with n=160, k=16 and d=52.
This code was found by Heurico 1.16 in 11.5 seconds.