The generator matrix

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

generates a code of length 71 over Z3[X]/(X^3) who´s minimum homogenous weight is 129.

Homogenous weight enumerator: w(x)=1x^0+108x^129+18x^130+72x^131+524x^132+870x^133+198x^134+1580x^135+2202x^136+648x^137+3846x^138+6054x^139+1512x^140+7598x^141+8412x^142+2016x^143+7734x^144+7440x^145+1116x^146+3288x^147+2454x^148+198x^149+514x^150+222x^151+54x^152+162x^153+24x^154+18x^155+64x^156+6x^157+28x^159+24x^162+16x^165+10x^168+12x^171+4x^174+2x^177

The gray image is a linear code over GF(3) with n=639, k=10 and d=387.
This code was found by Heurico 1.16 in 11.1 seconds.