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

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+102x^123+144x^124+144x^125+612x^126+186x^127+198x^128+966x^129+546x^130+630x^131+2892x^132+1548x^133+2430x^134+4558x^135+1542x^136+684x^137+1004x^138+132x^139+162x^140+318x^141+156x^142+72x^143+262x^144+72x^145+36x^146+116x^147+42x^148+18x^149+72x^150+6x^151+28x^153+2x^162+2x^183

The gray image is a linear code over GF(3) with n=603, k=9 and d=369.
This code was found by Heurico 1.16 in 2.16 seconds.