The generator matrix

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

generates a code of length 44 over Z3[X]/(X^3) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+270x^80+168x^81+378x^82+894x^83+738x^84+1188x^85+2484x^86+1884x^87+2430x^88+3192x^89+1950x^90+1728x^91+1716x^92+324x^93+108x^94+144x^95+6x^96+30x^98+6x^99+18x^101+12x^102+8x^108+6x^111

The gray image is a linear code over GF(3) with n=396, k=9 and d=240.
This code was found by Heurico 1.16 in 14.1 seconds.