The generator matrix

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

generates a code of length 69 over Z3[X]/(X^3) who´s minimum homogenous weight is 130.

Homogenous weight enumerator: w(x)=1x^0+990x^130+1746x^131+1314x^132+3882x^133+4644x^134+2222x^135+7218x^136+6708x^137+2956x^138+6234x^139+6336x^140+2222x^141+4746x^142+3558x^143+1096x^144+1914x^145+738x^146+138x^147+222x^148+36x^149+10x^150+48x^151+36x^152+12x^154+6x^155+2x^156+6x^157+6x^161+2x^162

The gray image is a linear code over GF(3) with n=621, k=10 and d=390.
This code was found by Heurico 1.16 in 85.6 seconds.