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

generates a code of length 59 over Z3[X]/(X^3) who´s minimum homogenous weight is 114.

Homogenous weight enumerator: w(x)=1x^0+20x^114+54x^116+20x^117+486x^118+108x^119+28x^120+10x^123+2x^174

The gray image is a linear code over GF(3) with n=531, k=6 and d=342.
This code was found by Heurico 1.16 in 0.0646 seconds.