The generator matrix

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

generates a code of length 5 over Z16 who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+23x^2+44x^3+168x^4+552x^5+168x^6+44x^7+23x^8+1x^10

The gray image is a code over GF(2) with n=40, k=10 and d=8.
This code was found by Heurico 1.16 in 0.000341 seconds.