The generator matrix

 1  0  1  1  1
 0  1  1  0  0
 0  0 24  0  3
 0  0  0  3  3

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

Homogenous weight enumerator: w(x)=1x^0+78x^4+524x^6+468x^7+5670x^8+2036x^9+36252x^10+11340x^11+2046x^12+624x^13+10x^15

The gray image is a code over GF(3) with n=45, k=10 and d=12.
This code was found by Heurico 1.16 in 0.0958 seconds.