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

generates a code of length 36 over Z3[X]/(X^3) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+70x^57+188x^60+242x^63+384x^66+1224x^69+15308x^72+1562x^75+258x^78+198x^81+136x^84+58x^87+44x^90+8x^93+2x^99

The gray image is a linear code over GF(3) with n=324, k=9 and d=171.
This code was found by Heurico 1.16 in 1.54 seconds.