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

generates a code of length 70 over Z3[X]/(X^3) who´s minimum homogenous weight is 129.

Homogenous weight enumerator: w(x)=1x^0+136x^129+156x^130+168x^131+500x^132+282x^133+282x^134+684x^135+780x^136+936x^137+2038x^138+2052x^139+2988x^140+3442x^141+1914x^142+1164x^143+422x^144+366x^145+138x^146+336x^147+120x^148+96x^149+212x^150+84x^151+30x^152+192x^153+60x^154+24x^155+42x^156+12x^157+6x^158+4x^159+6x^160+6x^162+2x^165+2x^192

The gray image is a linear code over GF(3) with n=630, k=9 and d=387.
This code was found by Heurico 1.16 in 2.28 seconds.