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

generates a code of length 39 over Z3[X]/(X^3) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+42x^66+94x^69+140x^72+94x^75+5910x^78+60x^81+64x^84+54x^87+50x^90+34x^93+8x^96+8x^99+2x^117

The gray image is a linear code over GF(3) with n=351, k=8 and d=198.
This code was found by Heurico 1.16 in 0.208 seconds.