The generator matrix

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

generates a code of length 38 over Z3[X]/(X^3) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+150x^68+294x^69+324x^70+546x^71+894x^72+1944x^73+1158x^74+2412x^75+3888x^76+1452x^77+2376x^78+2592x^79+912x^80+508x^81+138x^83+50x^84+18x^86+6x^87+8x^90+2x^93+6x^96+2x^99+2x^102

The gray image is a linear code over GF(3) with n=342, k=9 and d=204.
This code was found by Heurico 1.16 in 0.724 seconds.