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

generates a code of length 68 over Z3[X]/(X^3) who´s minimum homogenous weight is 123.

Homogenous weight enumerator: w(x)=1x^0+44x^123+154x^126+226x^129+318x^132+1458x^134+496x^135+2916x^137+412x^138+310x^141+90x^144+36x^147+16x^150+24x^153+20x^156+12x^159+16x^162+8x^165+2x^168+2x^180

The gray image is a linear code over GF(3) with n=612, k=8 and d=369.
This code was found by Heurico 1.16 in 0.495 seconds.