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

generates a code of length 59 over Z3[X]/(X^3) who´s minimum homogenous weight is 108.

Homogenous weight enumerator: w(x)=1x^0+248x^108+162x^114+908x^117+4374x^118+648x^120+120x^126+84x^135+14x^144+2x^171

The gray image is a linear code over GF(3) with n=531, k=8 and d=324.
This code was found by Heurico 1.16 in 6.48 seconds.