The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+31x^2+221x^4+771x^6+771x^8+221x^10+31x^12+1x^14

The gray image is a code over GF(2) with n=14, k=11 and d=2.
This code was found by Heurico 1.16 in 0.00444 seconds.