The generator matrix

 1  0  0  1
 0  1  0  7
 0  0  1  5
 0  0  0  6

generates a code of length 4 over Z9 who´s minimum homogenous weight is 3.

Homogenous weight enumerator: w(x)=1x^0+8x^3+108x^4+240x^6+432x^7+486x^8+464x^9+432x^10+16x^12

The gray image is a code over GF(3) with n=12, k=7 and d=3.
This code was found by Heurico 1.16 in 0.000487 seconds.