The generator matrix

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

generates a code of length 39 over Z3[X]/(X^3) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+234x^72+312x^73+2304x^74+1776x^75+1434x^76+3132x^77+2124x^78+1632x^79+2790x^80+1630x^81+648x^82+1302x^83+294x^84+12x^85+24x^86+12x^87+12x^88+6x^89+4x^90

The gray image is a linear code over GF(3) with n=351, k=9 and d=216.
This code was found by Heurico 1.16 in 0.463 seconds.