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

generates a code of length 45 over Z3[X]/(X^3) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+130x^75+212x^78+18x^80+202x^81+180x^83+246x^84+720x^86+204x^87+1440x^89+13388x^90+1440x^92+200x^93+576x^95+192x^96+206x^99+150x^102+88x^105+54x^108+28x^111+6x^114+2x^120

The gray image is a linear code over GF(3) with n=405, k=9 and d=225.
This code was found by Heurico 1.16 in 3.06 seconds.