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

generates a code of length 42 over Z3[X]/(X^3) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+114x^69+192x^72+310x^75+608x^78+1124x^81+14896x^84+1336x^87+580x^90+220x^93+142x^96+70x^99+72x^102+14x^105+4x^108

The gray image is a linear code over GF(3) with n=378, k=9 and d=207.
This code was found by Heurico 1.16 in 2.02 seconds.