The generator matrix

 1  0  1  1  1  1  1
 0  1  1  2  0 2X^2+2X+1  0
 0  0 2X  0  X X^2+2X X^2
 0  0  0  X  X 2X X^2+2X

generates a code of length 7 over Z3[X]/(X^3) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+108x^8+130x^9+648x^10+648x^11+7446x^12+2592x^13+28998x^14+14850x^15+2592x^16+864x^17+166x^18+6x^21

The gray image is a linear code over GF(3) with n=63, k=10 and d=24.
This code was found by Heurico 1.16 in 0.216 seconds.