The generator matrix

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

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+66x^81+54x^82+330x^83+552x^84+432x^85+936x^86+2086x^87+1296x^88+1956x^89+3766x^90+1728x^91+1830x^92+2724x^93+864x^94+648x^95+230x^96+114x^98+22x^99+18x^101+12x^102+2x^105+6x^108+6x^111+4x^114

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 0.776 seconds.