The generator matrix

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

generates a code of length 41 over Z3[X]/(X^3) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+192x^73+294x^74+148x^75+552x^76+792x^77+820x^78+978x^79+2034x^80+2604x^81+2370x^82+2760x^83+2770x^84+1116x^85+924x^86+128x^87+402x^88+324x^89+68x^90+156x^91+150x^92+14x^93+60x^94+12x^95+6x^96+6x^97+2x^102

The gray image is a linear code over GF(3) with n=369, k=9 and d=219.
This code was found by Heurico 1.16 in 1.13 seconds.