The generator matrix

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

generates a code of length 69 over Z3[X]/(X^3) who´s minimum homogenous weight is 129.

Homogenous weight enumerator: w(x)=1x^0+246x^129+462x^130+1416x^131+3078x^132+2646x^133+3882x^134+5242x^135+4422x^136+5592x^137+5422x^138+5166x^139+5472x^140+4856x^141+3348x^142+2910x^143+2626x^144+816x^145+600x^146+542x^147+150x^148+24x^149+64x^150+12x^152+28x^153+18x^155+6x^156+2x^162

The gray image is a linear code over GF(3) with n=621, k=10 and d=387.
This code was found by Heurico 1.16 in 8.22 seconds.