The generator matrix

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

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+774x^80+1838x^81+5100x^82+7176x^83+13744x^84+20028x^85+24918x^86+37240x^87+48378x^88+56076x^89+70648x^90+70158x^91+59034x^92+49160x^93+34278x^94+16872x^95+9998x^96+4248x^97+1254x^98+296x^99+36x^100+84x^101+42x^102+18x^103+24x^104+12x^105+6x^106

The gray image is a linear code over GF(3) with n=405, k=12 and d=240.
This code was found by Heurico 1.16 in 341 seconds.