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

generates a code of length 44 over Z3[X]/(X^3) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+162x^81+96x^82+132x^83+418x^84+294x^85+936x^86+684x^87+762x^88+1728x^89+578x^90+198x^91+60x^92+172x^93+48x^94+18x^95+132x^96+48x^97+36x^98+30x^99+12x^100+6x^101+8x^102+2x^120

The gray image is a linear code over GF(3) with n=396, k=8 and d=243.
This code was found by Heurico 1.16 in 0.171 seconds.