The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+60x^14+288x^15+641x^16+1548x^17+2601x^18+7054x^19+8126x^20+7330x^21+2859x^22+1388x^23+474x^24+272x^25+79x^26+38x^27+6x^28+2x^29+1x^30

The gray image is a code over GF(2) with n=160, k=15 and d=56.
This code was found by Heurico 1.16 in 3.29 seconds.