The generator matrix
1 1 1 1
0 3 24 9
generates a code of length 4 over Z27 who´s minimum homogenous weight is 6.
Homogenous weight enumerator: w(x)=1x^0+14x^6+12x^7+180x^8+28x^9+6x^10+2x^12
The gray image is a code over GF(3) with n=36, k=5 and d=18.
This code was found by Heurico 1.16 in 7.3e-005 seconds.