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

generates a code of length 58 over Z3[X]/(X^3) who´s minimum homogenous weight is 113.

Homogenous weight enumerator: w(x)=1x^0+108x^113+198x^114+348x^117+16x^120+54x^122+2x^135+2x^147

The gray image is a linear code over GF(3) with n=522, k=6 and d=339.
This code was found by Heurico 1.16 in 0.196 seconds.