The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+52x^13+125x^14+170x^15+239x^16+378x^17+785x^18+3520x^19+5874x^20+3434x^21+810x^22+436x^23+264x^24+158x^25+70x^26+32x^27+22x^28+10x^29+1x^30+2x^31+1x^34

The gray image is a code over GF(2) with n=160, k=14 and d=52.
This code was found by Heurico 1.16 in 1.76 seconds.