The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+22x^13+61x^14+112x^15+104x^16+312x^17+323x^18+1072x^19+4146x^20+1108x^21+328x^22+336x^23+94x^24+88x^25+52x^26+16x^27+6x^28+6x^29+3x^30+1x^32+1x^34

The gray image is a code over GF(2) with n=160, k=13 and d=52.
This code was found by Heurico 1.16 in 3.54 seconds.