The generator matrix

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

generates a code of length 38 over Z3[X]/(X^3) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+240x^70+312x^71+2154x^72+1512x^73+2148x^74+2782x^75+1992x^76+2166x^77+2414x^78+1566x^79+840x^80+1298x^81+180x^82+30x^83+14x^84+6x^85+12x^86+4x^87+12x^88

The gray image is a linear code over GF(3) with n=342, k=9 and d=210.
This code was found by Heurico 1.16 in 0.452 seconds.