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

generates a code of length 62 over Z3[X]/(X^3) who´s minimum homogenous weight is 124.

Homogenous weight enumerator: w(x)=1x^0+54x^124+14x^126+2x^129+8x^132+2x^135

The gray image is a linear code over GF(3) with n=558, k=4 and d=372.
This code was found by Heurico 1.16 in 0.0723 seconds.