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

generates a code of length 45 over Z3[X]/(X^3) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+216x^86+250x^87+162x^88+354x^89+414x^90+138x^91+342x^92+198x^93+12x^95+14x^96+18x^97+24x^98+12x^99+6x^100+18x^101+6x^104+2x^117

The gray image is a linear code over GF(3) with n=405, k=7 and d=258.
This code was found by Heurico 1.16 in 8 seconds.