The generator matrix

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

generates a code of length 69 over Z3[X]/(X^3) who´s minimum homogenous weight is 127.

Homogenous weight enumerator: w(x)=1x^0+198x^127+108x^128+580x^129+1134x^130+1170x^131+2374x^132+2190x^133+3528x^134+4632x^135+3558x^136+6048x^137+6756x^138+4560x^139+6498x^140+6018x^141+2826x^142+2682x^143+1854x^144+1062x^145+378x^146+238x^147+282x^148+64x^150+168x^151+54x^153+42x^154+20x^156+18x^157+2x^159+2x^162+2x^174+2x^177

The gray image is a linear code over GF(3) with n=621, k=10 and d=381.
This code was found by Heurico 1.16 in 10.9 seconds.