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

generates a code of length 67 over Z3[X]/(X^3) who´s minimum homogenous weight is 129.

Homogenous weight enumerator: w(x)=1x^0+38x^129+24x^130+178x^132+84x^133+1620x^134+100x^135+36x^136+56x^138+12x^139+26x^141+6x^142+4x^144+2x^201

The gray image is a linear code over GF(3) with n=603, k=7 and d=387.
This code was found by Heurico 1.16 in 0.162 seconds.