The generator matrix

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

generates a code of length 20 over Z16 who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+92x^14+8x^15+326x^16+136x^17+888x^18+1392x^19+2489x^20+1392x^21+959x^22+136x^23+245x^24+8x^25+107x^26+11x^28+1x^30+1x^34

The gray image is a code over GF(2) with n=160, k=13 and d=56.
This code was found by Heurico 1.16 in 2.68 seconds.