The generator matrix

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

generates a code of length 67 over Z3[X]/(X^3) who´s minimum homogenous weight is 124.

Homogenous weight enumerator: w(x)=1x^0+318x^124+546x^125+700x^126+1392x^127+1860x^128+2926x^129+3138x^130+3708x^131+5940x^132+5142x^133+5124x^134+7654x^135+5874x^136+4290x^137+4544x^138+2394x^139+1464x^140+736x^141+408x^142+288x^143+36x^144+168x^145+114x^146+36x^147+84x^148+84x^149+20x^150+36x^151+18x^152+6x^153

The gray image is a linear code over GF(3) with n=603, k=10 and d=372.
This code was found by Heurico 1.16 in 46.3 seconds.