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

generates a code of length 38 over Z3[X]/(X^3) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+156x^67+156x^68+308x^69+588x^70+378x^71+934x^72+702x^73+2226x^74+2340x^75+2904x^76+3822x^77+2426x^78+882x^79+474x^80+368x^81+390x^82+168x^83+144x^84+162x^85+54x^86+38x^87+42x^88+12x^89+6x^91+2x^99

The gray image is a linear code over GF(3) with n=342, k=9 and d=201.
This code was found by Heurico 1.16 in 1.04 seconds.