The generator matrix

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

generates a code of length 10 over Z16 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+55x^4+146x^5+261x^6+580x^7+993x^8+3390x^9+21965x^10+3320x^11+965x^12+622x^13+295x^14+132x^15+34x^16+2x^17+7x^18

The gray image is a code over GF(2) with n=80, k=15 and d=16.
This code was found by Heurico 1.16 in 0.366 seconds.