The generator matrix
1 1 1 1 1
0 X 2X 0 0
0 0 X^2 0 0
0 0 0 X^2 0
0 0 0 0 X^2
generates a code of length 5 over Z3[X]/(X^3) who´s minimum homogenous weight is 3.
Homogenous weight enumerator: w(x)=1x^0+10x^3+18x^4+40x^6+108x^7+324x^8+80x^9+5076x^10+648x^11+80x^12+144x^13+32x^15
The gray image is a linear code over GF(3) with n=45, k=8 and d=9.
This code was found by Heurico 1.16 in 0.00255 seconds.