The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+38x^5+145x^6+368x^7+1508x^8+7782x^9+13071x^10+7792x^11+1524x^12+370x^13+127x^14+32x^15+7x^16+2x^17+1x^18

The gray image is a code over GF(2) with n=80, k=15 and d=20.
This code was found by Heurico 1.16 in 11.7 seconds.