The generator matrix

 1  1  1  1  1  1  1  1  1  2  1 12  2  8  1  1  1  4  1  1
 0  2  0  0  0  8  8  8  8  2 10  2  4  2 12 14  6 12  6  4
 0  0  2  0  0 12  6  2  2 10  6 12  0 12 12 14  4  2  8  4
 0  0  0  2  0  6  6  6  4 12 12  4 12  2  8 14  2  8 14  4
 0  0  0  0  2  2  4  6  2  4 12  6 14  4 12  0 10  6 12 10

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

Homogenous weight enumerator: w(x)=1x^0+124x^14+610x^15+1304x^16+2818x^17+6014x^18+12514x^19+18334x^20+13008x^21+6205x^22+2830x^23+1113x^24+410x^25+168x^26+62x^27+16x^28+4x^29+1x^30

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 12.4 seconds.