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

generates a code of length 45 over Z3[X]/(X^3) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+518x^84+162x^86+864x^87+486x^88+648x^89+1136x^90+972x^91+648x^92+656x^93+216x^96+184x^99+68x^102+2x^117

The gray image is a linear code over GF(3) with n=405, k=8 and d=252.
This code was found by Heurico 1.16 in 4.8 seconds.