The generator matrix

 1  0  1  1  1 14  1  1  8  8  6  2  1
 0  1 11  6  1  1  3  0  1  1  1 14  6
 0  0 12  0  0  0  0  4  8  4  4  4  4
 0  0  0 12  0  4  4  4  8  4 12  4  8
 0  0  0  0  4  0  4  0  4 12  8  4 12
 0  0  0  0  0  8  0  0  8  8  8  0  8
 0  0  0  0  0  0  8  8  8  8  0  0  0

generates a code of length 13 over Z16 who´s minimum homogenous weight is 7.

Homogenous weight enumerator: w(x)=1x^0+34x^7+170x^8+336x^9+1148x^10+4758x^11+17076x^12+18404x^13+17176x^14+4782x^15+1157x^16+328x^17+108x^18+26x^19+28x^20+4x^21

The gray image is a code over GF(2) with n=104, k=16 and d=28.
This code was found by Heurico 1.16 in 13.1 seconds.