The generator matrix

 1  1  1  1  1  1  2  2  1  1
 0 12  0  0  0  0  8 12  0 12
 0  0 12  0  0  0 12  8  4 12
 0  0  0 12  0  4  4  4 12  0
 0  0  0  0 12  4  0 12  8 12
 0  0  0  0  0  8  8  0  0  8

generates a code of length 10 over Z16 who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+36x^5+97x^6+152x^7+356x^8+828x^9+5231x^10+848x^11+372x^12+156x^13+79x^14+24x^15+7x^16+4x^17+1x^18

The gray image is a code over GF(2) with n=80, k=13 and d=20.
This code was found by Heurico 1.16 in 1.67 seconds.