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

generates a code of length 69 over Z3[X]/(X^3) who´s minimum homogenous weight is 128.

Homogenous weight enumerator: w(x)=1x^0+396x^128+230x^129+636x^131+354x^132+1770x^134+740x^135+972x^136+3810x^137+2574x^138+1944x^139+3582x^140+720x^141+618x^143+210x^144+396x^146+144x^147+246x^149+76x^150+132x^152+46x^153+78x^155+2x^156+2x^159+2x^165+2x^189

The gray image is a linear code over GF(3) with n=621, k=9 and d=384.
This code was found by Heurico 1.16 in 22.5 seconds.