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  X  1  1  1  X  0  1  1  X  X
 0  X 2X  0 2X^2+X 2X X^2+2X X^2 2X^2+X 2X^2+X  0 2X 2X^2+X  0 2X X^2+2X 2X^2 X^2+X 2X^2+X  0 2X^2+2X X^2+X X^2  X 2X^2  X 2X^2+X X^2 2X^2+X 2X  X  X 2X  X  0 2X^2+X 2X^2+X 2X^2+X
 0  0 X^2  0  0  0 2X^2  0 2X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 2X^2 2X^2 X^2  0 X^2 X^2 2X^2  0 X^2  0 X^2  0 2X^2 X^2  0 2X^2 2X^2 X^2 2X^2 X^2
 0  0  0 X^2  0 X^2 2X^2 2X^2 2X^2 X^2  0 2X^2  0 2X^2 2X^2 2X^2  0 2X^2  0  0 X^2 X^2 2X^2  0  0 X^2  0 2X^2 2X^2 X^2 2X^2 X^2 X^2 2X^2 2X^2 X^2 2X^2 X^2
 0  0  0  0 2X^2 2X^2 X^2  0 2X^2 X^2 2X^2 2X^2  0  0 2X^2  0 X^2  0 2X^2 2X^2 2X^2  0 X^2 2X^2  0 2X^2 X^2 2X^2 2X^2  0 X^2  0 2X^2 X^2  0  0 2X^2 2X^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+284x^69+54x^70+450x^72+324x^73+972x^74+438x^75+648x^76+1944x^77+526x^78+432x^79+322x^81+102x^84+46x^87+8x^90+8x^96+2x^99

The gray image is a linear code over GF(3) with n=342, k=8 and d=207.
This code was found by Heurico 1.16 in 10.6 seconds.