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

generates a code of length 61 over Z3[X]/(X^3) who´s minimum homogenous weight is 119.

Homogenous weight enumerator: w(x)=1x^0+108x^119+194x^120+356x^123+8x^126+54x^128+2x^129+4x^132+2x^156

The gray image is a linear code over GF(3) with n=549, k=6 and d=357.
This code was found by Heurico 1.16 in 0.246 seconds.