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

generates a code of length 43 over Z3[X]/(X^3) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+350x^78+54x^79+162x^80+1376x^81+594x^82+972x^83+2890x^84+1782x^85+1944x^86+3782x^87+1728x^88+1296x^89+2184x^90+216x^91+258x^93+38x^96+42x^99+6x^105+6x^108+2x^111

The gray image is a linear code over GF(3) with n=387, k=9 and d=234.
This code was found by Heurico 1.16 in 0.736 seconds.