The generator matrix

1 0 0 0 0 1 1
0 1 0 0 0 1 0
0 0 1 0 0 1 0
0 0 0 1 0 1 0
0 0 0 0 1 1 0

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

Homogenous weight enumerator: w(x)=1x^0+20x^2+10x^3+110x^4+120x^5+125x^6+252x^7+125x^8+120x^9+110x^10+10x^11+20x^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 1.10 in 0 seconds.