The generator matrix

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

generates a code of length 45 over Z3[X]/(X^3) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+318x^82+312x^83+1694x^84+3342x^85+2844x^86+5154x^87+5442x^88+5010x^89+8436x^90+7158x^91+5412x^92+6144x^93+4374x^94+1416x^95+1104x^96+690x^97+48x^98+44x^99+48x^100+18x^101+22x^102+6x^103+6x^104+6x^106

The gray image is a linear code over GF(3) with n=405, k=10 and d=246.
This code was found by Heurico 1.16 in 4.99 seconds.