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

generates a code of length 67 over Z3[X]/(X^3) who´s minimum homogenous weight is 126.

Homogenous weight enumerator: w(x)=1x^0+270x^126+590x^129+870x^132+2916x^134+992x^135+550x^138+144x^141+128x^144+64x^147+30x^150+2x^153+2x^156+2x^189

The gray image is a linear code over GF(3) with n=603, k=8 and d=378.
This code was found by Heurico 1.16 in 0.434 seconds.