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

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+234x^124+306x^125+124x^126+498x^127+558x^128+198x^129+1134x^130+1284x^131+1034x^132+3048x^133+3168x^134+1970x^135+2928x^136+1266x^137+166x^138+420x^139+336x^140+70x^141+186x^142+186x^143+38x^144+150x^145+120x^146+30x^147+84x^148+54x^149+12x^150+60x^151+12x^152+6x^154+2x^183

The gray image is a linear code over GF(3) with n=603, k=9 and d=372.
This code was found by Heurico 1.16 in 88.6 seconds.