The generator matrix

 1  0  1  1  1  1  1 2X^2  1  1  1 2X^2+2X  1 2X^2+X  1  1  1  1  1 2X^2+X  1  1 2X^2  1  1  1  1  1 2X^2+X 2X^2  1 X^2  1 2X  1 2X^2  X  1
 0  1  1  2 2X^2 2X+1  2  1  0 2X+1 2X^2+2  1 2X  1 X+1  2 2X^2+X X^2+2 2X^2+X+1  1 X+2 2X^2+X+1  1 2X^2 2X^2+X+2  X X+2 X^2+2  1  1 2X^2+X+2  X  1  1 X+2  1 2X^2+X 2X^2+2
 0  0 2X  0 2X^2  0  X 2X^2+X 2X^2 2X^2+X 2X^2+2X 2X 2X^2+2X 2X X^2 X^2+2X X^2+2X X^2+X X^2+X  0  X X^2+2X 2X^2+X  X 2X 2X X^2+X 2X^2 2X^2+2X  0 X^2 X^2+X X^2+X 2X  X 2X^2+X X^2+X 2X^2+X
 0  0  0  X 2X^2+X X^2+X  X 2X^2+2X X^2+2X 2X 2X^2+X  X X^2+2X X^2 X^2+2X 2X^2 X^2 2X^2+2X  0 2X^2+2X X^2 X^2+X 2X^2+X 2X^2 X^2+2X X^2+X 2X 2X X^2+2X X^2+X  0 X^2+2X  0 X^2+2X 2X^2+X X^2+X  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+216x^67+276x^68+846x^69+1470x^70+1716x^71+3384x^72+3630x^73+4902x^74+7964x^75+7746x^76+7632x^77+8496x^78+4818x^79+2682x^80+1652x^81+864x^82+228x^83+206x^84+174x^85+48x^86+36x^87+30x^88+12x^89+12x^90+6x^91+2x^93

The gray image is a linear code over GF(3) with n=342, k=10 and d=201.
This code was found by Heurico 1.16 in 4.98 seconds.