The generator matrix

 1  0  1  1
 0  1  7  0
 0  0  9  0
 0  0  0  9

generates a code of length 4 over Z27 who´s minimum homogenous weight is 3.

Homogenous weight enumerator: w(x)=1x^0+8x^3+72x^4+456x^6+288x^7+4536x^8+896x^9+288x^10+16x^12

The gray image is a code over GF(3) with n=36, k=8 and d=9.
This code was found by Heurico 1.16 in 0.00127 seconds.