The generator matrix

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

generates a code of length 45 over Z3[X]/(X^3) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+84x^80+94x^81+522x^82+960x^83+1386x^84+1512x^85+3696x^86+4010x^87+3546x^88+9486x^89+7904x^90+4506x^91+9942x^92+5646x^93+2496x^94+1692x^95+550x^96+378x^97+276x^98+50x^99+138x^100+78x^101+24x^102+24x^103+30x^104+10x^105+6x^108+2x^114

The gray image is a linear code over GF(3) with n=405, k=10 and d=240.
This code was found by Heurico 1.16 in 6.1 seconds.