The generator matrix

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

generates a code of length 38 over Z3[X]/(X^3) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+828x^72+630x^73+378x^74+1260x^75+720x^76+540x^77+1152x^78+558x^79+54x^80+340x^81+36x^82+36x^84+18x^87+8x^90+2x^99

The gray image is a linear code over GF(3) with n=342, k=8 and d=216.
This code was found by Heurico 1.16 in 42.2 seconds.