The generator matrix

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

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+816x^81+1188x^82+2340x^83+5178x^84+6174x^85+9054x^86+13098x^87+15732x^88+18774x^89+23362x^90+22194x^91+20880x^92+16860x^93+10458x^94+5634x^95+3420x^96+1116x^97+180x^98+526x^99+156x^102+6x^105

The gray image is a linear code over GF(3) with n=405, k=11 and d=243.
This code was found by Heurico 1.16 in 43 seconds.