The generator matrix

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

generates a code of length 7 over Z3[X]/(X^3) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+36x^10+90x^11+28x^12+144x^13+1602x^14+48x^15+144x^16+90x^17+2x^18+2x^21

The gray image is a linear code over GF(3) with n=63, k=7 and d=30.
This code was found by Heurico 1.16 in 0.00141 seconds.