The generator matrix

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

generates a code of length 67 over Z3[X]/(X^3) who´s minimum homogenous weight is 123.

Homogenous weight enumerator: w(x)=1x^0+154x^123+168x^124+438x^125+1012x^126+1356x^127+1650x^128+3008x^129+3042x^130+3864x^131+4966x^132+5670x^133+6366x^134+6544x^135+5610x^136+5088x^137+4038x^138+2526x^139+1386x^140+992x^141+462x^142+78x^143+236x^144+84x^145+48x^146+112x^147+30x^148+24x^149+42x^150+12x^152+24x^153+6x^154+4x^156+2x^159+4x^162+2x^165

The gray image is a linear code over GF(3) with n=603, k=10 and d=369.
This code was found by Heurico 1.16 in 10.2 seconds.