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  1  1  1  1  1  X  1  1
 0  X 2X  0 2X^2+X 2X X^2+2X X^2 2X^2+X 2X^2+X  0 2X 2X^2+X  0 2X X^2+2X 2X^2 X^2+X 2X^2+X X^2  0 X^2+X 2X^2+2X  X 2X^2  X 2X^2+X X^2 X^2+2X  X X^2+2X 2X^2 2X  X X^2+2X  0  0 2X^2+X  X X^2+X X^2 X^2+X 2X^2+X X^2  0
 0  0 X^2  0  0  0 2X^2  0 2X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 2X^2 X^2 2X^2  0 X^2 X^2 2X^2  0 X^2  0 2X^2  0 2X^2 2X^2 2X^2 X^2  0 2X^2 2X^2 2X^2 2X^2 X^2 X^2  0  0  0 X^2
 0  0  0 X^2  0 X^2 2X^2 2X^2 2X^2 X^2  0 2X^2  0 2X^2 2X^2 2X^2  0 2X^2  0 2X^2  0 X^2 X^2  0  0 X^2  0 2X^2 2X^2  0 X^2 X^2  0 2X^2  0 2X^2 2X^2 X^2 X^2 2X^2 X^2 X^2 2X^2  0  0
 0  0  0  0 2X^2 2X^2 X^2  0 2X^2 X^2 2X^2 2X^2  0  0 2X^2  0 X^2  0 2X^2 X^2 2X^2  0 2X^2 2X^2  0 2X^2 X^2 2X^2 2X^2 X^2  0 X^2 X^2  0 X^2 2X^2  0  0 X^2 X^2  0 2X^2  0 X^2 X^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+30x^81+54x^82+162x^83+46x^84+102x^85+204x^86+50x^87+738x^88+186x^89+2942x^90+1380x^91+162x^92+32x^93+72x^94+126x^95+12x^96+36x^97+102x^98+18x^99+42x^100+18x^101+12x^102+6x^103+12x^104+8x^105+6x^108+2x^132

The gray image is a linear code over GF(3) with n=405, k=8 and d=243.
This code was found by Heurico 1.16 in 0.196 seconds.