The generator matrix

 1  1  2  1  1
 0 12 12  0  0
 0  0  8  0  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+7x^2+40x^4+160x^5+40x^6+7x^8+1x^10

The gray image is a code over GF(2) with n=40, k=8 and d=8.
This code was found by Heurico 1.16 in 9.39e-005 seconds.