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

generates a code of length 45 over Z3[X]/(X^3) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+434x^81+18x^82+1250x^84+144x^85+486x^86+1834x^87+1404x^88+1944x^89+3936x^90+2520x^91+1944x^92+2064x^93+288x^94+834x^96+440x^99+122x^102+12x^105+2x^108+2x^114+2x^117+2x^120

The gray image is a linear code over GF(3) with n=405, k=9 and d=243.
This code was found by Heurico 1.16 in 1.36 seconds.