The generator matrix
1 0 0 1
0 1 0 2X^2
0 0 1 2X^2
0 0 0 2X^2+X
generates a code of length 4 over Z3[X]/(X^3) who´s minimum homogenous weight is 2.
Homogenous weight enumerator: w(x)=1x^0+60x^2+8x^3+1350x^4+360x^5+16440x^6+5400x^7+114768x^8+32864x^9+5400x^10+480x^11+16x^12
The gray image is a linear code over GF(3) with n=36, k=11 and d=6.
This code was found by Heurico 1.16 in 0.318 seconds.