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

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+170x^78+390x^81+928x^84+2916x^86+1634x^87+216x^90+180x^93+82x^96+30x^99+8x^102+4x^105+2x^126

The gray image is a linear code over GF(3) with n=387, k=8 and d=234.
This code was found by Heurico 1.16 in 0.184 seconds.