The generator matrix

 1  1  1  1  1
 0  3  0  0 21
 0  0  3  0 15
 0  0  0  3 15

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

Homogenous weight enumerator: w(x)=1x^0+60x^4+200x^6+360x^7+810x^8+740x^9+14652x^10+1620x^11+750x^12+480x^13+10x^15

The gray image is a code over GF(3) with n=45, k=9 and d=12.
This code was found by Heurico 1.16 in 0.0202 seconds.