The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+127x^14+298x^16+64x^17+875x^18+1472x^19+2510x^20+1472x^21+911x^22+64x^23+272x^24+101x^26+22x^28+2x^30+1x^32

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 13.9 seconds.