The generator matrix

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

generates a code of length 43 over Z3[X]/(X^3) who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+114x^79+252x^80+36x^81+306x^82+498x^83+716x^84+420x^85+1554x^86+1382x^87+378x^88+378x^89+40x^90+108x^91+114x^92+4x^93+102x^94+84x^95+4x^96+30x^97+36x^98+2x^99+2x^117

The gray image is a linear code over GF(3) with n=387, k=8 and d=237.
This code was found by Heurico 1.16 in 0.176 seconds.