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

generates a code of length 36 over Z3[X]/(X^3) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+36x^60+94x^63+180x^66+444x^69+5102x^72+490x^75+54x^78+66x^81+46x^84+24x^87+18x^90+4x^93+2x^99

The gray image is a linear code over GF(3) with n=324, k=8 and d=180.
This code was found by Heurico 1.16 in 0.185 seconds.