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  X  1  1  1  1  X  X  X  1  1  X  1  1  1  X
 0  X  0  0  0 2X X^2 2X^2  0 X^2 2X^2  X 2X^2+2X 2X 2X^2+X X^2+X 2X^2+X 2X^2+2X X^2+2X 2X X^2+X 2X 2X^2+X X^2+2X 2X^2+X 2X X^2+X  0 2X^2+X 2X^2+X 2X^2+X  X 2X 2X^2 2X^2  0  X X^2+2X X^2+2X 2X^2+X 2X  0  X 2X^2 2X^2+X
 0  0  X  0 X^2 2X^2 2X^2+2X 2X^2+X X^2+2X 2X^2+X X^2+2X  X  X 2X^2+2X 2X^2 2X^2+X 2X^2+X X^2 X^2  X X^2+2X X^2+2X 2X X^2+2X X^2  X 2X 2X X^2+2X X^2+2X  0  0 X^2+2X  0 X^2  X X^2+X X^2 2X 2X^2+2X X^2+2X  X  0 2X^2+2X 2X^2+2X
 0  0  0  X 2X^2+2X  0 2X^2 X^2+2X 2X^2+X 2X^2+X 2X 2X^2+2X X^2 X^2 X^2+2X 2X^2+X 2X^2 2X^2+2X X^2+X 2X  0 X^2+X  X 2X 2X^2+X  X 2X X^2+2X 2X^2 X^2+X X^2 2X  0 X^2+X 2X X^2+X  0 2X  X X^2+2X X^2 2X^2+X  X X^2+2X 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+444x^81+36x^83+1218x^84+54x^85+648x^86+1686x^87+1458x^88+2538x^89+2852x^90+2754x^91+2556x^92+1884x^93+108x^94+54x^95+792x^96+400x^99+192x^102+6x^105+2x^117

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 1.66 seconds.