The generator matrix

 1  0  0  0  0  0  0  1
 0  1  0  0  0  0  0  1
 0  0  1  0  0  0  0  1
 0  0  0  1  0  0  0  1
 0  0  0  0  1  0  0  1
 0  0  0  0  0  1  0  1
 0  0  0  0  0  0  1  1
 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+120x^2+1820x^4+8008x^6+12870x^8+8008x^10+1820x^12+120x^14+1x^16

The gray image is a code over GF(2) with n=16, k=15 and d=2.
This code was found by Heurico 1.16 in 0.826 seconds.