The generator matrix

 1  0  0  1  1  1 14  1  1  1  2  1 10  1  0 12 12  1  1  1
 0  1  0  1  6 15  1  1 12 13  1  4  1  2  4  1  1 13  8  0
 0  0  1  1 11  2  3  1  2  4  1  1  6  3  1  9  4 14  4  0
 0  0  0 12  0  0  0  0  4  8 12  4  8  4  8 12  0 12  4  0
 0  0  0  0 12  4  4  8  0  8  4  4  8  8  4  8 12 12 12  0

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

Homogenous weight enumerator: w(x)=1x^0+37x^14+312x^15+1008x^16+2856x^17+6285x^18+13674x^19+17031x^20+13866x^21+6423x^22+2764x^23+891x^24+300x^25+55x^26+18x^27+13x^28+2x^29

The gray image is a code over GF(2) with n=160, k=16 and d=56.
This code was found by Heurico 1.16 in 7.15 seconds.