The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+93x^14+28x^15+462x^16+492x^17+1812x^18+3064x^19+4461x^20+3064x^21+1876x^22+492x^23+407x^24+28x^25+88x^26+11x^28+3x^30+2x^32

The gray image is a code over GF(2) with n=160, k=14 and d=56.
This code was found by Heurico 1.16 in 28.4 seconds.