The generator matrix

 1  1  1  1  1  1  1  1
 0  2  0  0  0  0  0  0
 0  0  2  0  0  0  0  0
 0  0  0  2  0  0  0  0
 0  0  0  0  2  0  0  0
 0  0  0  0  0  2  0  0
 0  0  0  0  0  0  2  0
 0  0  0  0  0  0  0  2

generates a code of length 8 over Z4 who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+8x^2+28x^4+56x^6+326x^8+56x^10+28x^12+8x^14+1x^16

The gray image is a code over GF(2) with n=16, k=9 and d=2.
This code was found by Heurico 1.16 in 0.000632 seconds.