The generator matrix

 1  0  1  1  1  4  1  0  1  1  1  6  1  1 12  8  2  1  1  1
 0  1  1  0  3  1  0  1  9  0  5  1  5  1  1  1 14 14  4  0
 0  0  2  0  2  4 14 10  0 14  4 14  2  2  0  4  2  2  0  8
 0  0  0  2  2  6 14  2  2 12  0  8  8 14  2  4 12 10 12  8
 0  0  0  0  4  0  8  0 12  4  4  0  4  8  4  8  0 12  8  0

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

Homogenous weight enumerator: w(x)=1x^0+84x^14+296x^15+961x^16+2354x^17+6136x^18+14130x^19+17408x^20+14484x^21+6116x^22+2252x^23+918x^24+250x^25+112x^26+26x^27+8x^28

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 8.64 seconds.