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

generates a code of length 38 over Z3[X]/(X^3) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+96x^66+144x^69+54x^70+98x^72+324x^73+100x^75+5022x^76+60x^78+432x^79+60x^81+48x^84+56x^87+28x^90+24x^93+8x^96+2x^99+2x^102+2x^105

The gray image is a linear code over GF(3) with n=342, k=8 and d=198.
This code was found by Heurico 1.16 in 13.6 seconds.