The generator matrix

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

generates a code of length 6 over Z4 who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+30x^2+32x^3+127x^4+224x^5+196x^6+224x^7+127x^8+32x^9+30x^10+1x^12

The gray image is a code over GF(2) with n=12, k=10 and d=2.
This code was found by Heurico 1.16 in 0.0012 seconds.