The generator matrix

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

generates a code of length 39 over Z3[X]/(X^3) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+192x^71+314x^72+828x^73+1332x^74+1216x^75+1404x^76+3366x^77+1932x^78+2484x^79+3390x^80+1452x^81+1116x^82+246x^83+168x^84+144x^86+12x^87+72x^89+4x^90+6x^92+2x^99+2x^102

The gray image is a linear code over GF(3) with n=351, k=9 and d=213.
This code was found by Heurico 1.16 in 0.635 seconds.