The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+42x^2+511x^4+1484x^6+1519x^8+490x^10+49x^12

The gray image is a code over GF(2) with n=14, k=12 and d=2.
This code was found by Heurico 1.10 in 0 seconds.