The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+34x^7+172x^8+632x^9+1758x^10+6250x^11+12938x^12+22016x^13+12870x^14+6230x^15+1795x^16+648x^17+154x^18+30x^19+6x^20+2x^22

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 7.84 seconds.