The generator matrix

 1  0  0  1
 0  1  0 16
 0  0  1 14
 0  0  0 18

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

Homogenous weight enumerator: w(x)=1x^0+8x^3+432x^4+6072x^6+1728x^7+36936x^8+12128x^9+1728x^10+16x^12

The gray image is a code over GF(3) with n=36, k=10 and d=9.
This code was found by Heurico 1.16 in 0.0691 seconds.