The generator matrix

 1  1  1  1  1  1  1  1  1  2  1  2  1  2  1  1  1  2  1  1
 0 12  0  0  0  0  0  0  0 12 12  8  4 12  4 12 12  8 12 12
 0  0 12  0  0  0  4 12  4 12  4 12  4  8  8  4 12  0  0  0
 0  0  0 12  0  4  4  4  8  4  4  4  0 12  8  4  0  4  4 12
 0  0  0  0 12  4  0  4  4  0  8  0  8  4 12 12  4  0  8 12
 0  0  0  0  0  8  0  0  8  8  0  8  8  0  8  0  8  0  0  0
 0  0  0  0  0  0  8  0  0  0  0  8  8  0  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+38x^13+114x^14+202x^15+287x^16+458x^17+794x^18+1330x^19+9872x^20+1374x^21+858x^22+478x^23+254x^24+174x^25+86x^26+38x^27+16x^28+4x^29+4x^30+2x^32

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 1.09 seconds.