The generator matrix

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

generates a code of length 7 over Z4 who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+28x^2+10x^3+86x^4+120x^5+141x^6+252x^7+141x^8+120x^9+86x^10+10x^11+28x^12+1x^14

The gray image is a code over GF(2) with n=14, k=10 and d=2.
This code was found by Heurico 1.16 in 0.00133 seconds.