The generator matrix

 1  1  1  1  1
 0  3  0 21  0
 0  0  3  6  0
 0  0  0  9 18

generates a code of length 5 over Z27 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+18x^4+92x^6+108x^7+162x^8+308x^9+5076x^10+324x^11+318x^12+144x^13+10x^15

The gray image is a code over GF(3) with n=45, k=8 and d=12.
This code was found by Heurico 1.16 in 0.00248 seconds.