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

generates a code of length 69 over Z3[X]/(X^3) who´s minimum homogenous weight is 131.

Homogenous weight enumerator: w(x)=1x^0+324x^131+238x^132+924x^134+116x^135+2034x^137+114x^138+2022x^140+94x^141+324x^143+66x^144+78x^146+12x^147+48x^149+82x^150+48x^152+4x^153+30x^155+2x^180

The gray image is a linear code over GF(3) with n=621, k=8 and d=393.
This code was found by Heurico 1.16 in 23.9 seconds.