The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+61x^4+216x^6+32x^7+802x^8+992x^9+3984x^10+992x^11+802x^12+32x^13+216x^14+61x^16+1x^20

The gray image is a code over GF(2) with n=80, k=13 and d=16.
This code was found by Heurico 1.16 in 0.0147 seconds.