The generator matrix

 1  1  1  1
 0  3  0 21
 0  0  3 15
 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+108x^4+240x^6+432x^7+4860x^8+464x^9+432x^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 0.00221 seconds.