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

generates a code of length 62 over Z3[X]/(X^3) who´s minimum homogenous weight is 117.

Homogenous weight enumerator: w(x)=1x^0+28x^117+216x^119+228x^120+714x^123+696x^126+270x^128+12x^129+2x^138+4x^141+4x^144+6x^147+2x^150+4x^156

The gray image is a linear code over GF(3) with n=558, k=7 and d=351.
This code was found by Heurico 1.16 in 0.115 seconds.