The generator matrix
1 0 1 1
0 1 1 0
0 0 2X X
generates a code of length 4 over Z3[X]/(X^2) who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+6x^4+48x^6+24x^7+54x^8+80x^9+24x^10+6x^12
The gray image is a linear code over GF(3) with n=12, k=5 and d=4.
This code was found by Heurico 1.16 in 4.6e-005 seconds.