The generator matrix

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

generates a code of length 38 over Z3[X]/(X^3) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+832x^69+990x^70+1818x^71+4358x^72+4158x^73+4950x^74+8560x^75+5562x^76+8046x^77+9278x^78+4518x^79+2610x^80+2236x^81+810x^82+72x^83+206x^84+42x^87+2x^99

The gray image is a linear code over GF(3) with n=342, k=10 and d=207.
This code was found by Heurico 1.16 in 4.1 seconds.