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

generates a code of length 79 over Z3[X]/(X^3) who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+40x^144+24x^145+84x^146+230x^147+144x^148+258x^149+456x^150+210x^151+630x^152+972x^153+198x^154+2184x^155+1808x^156+198x^157+3708x^158+2348x^159+192x^160+2508x^161+1512x^162+216x^163+606x^164+314x^165+144x^166+132x^167+158x^168+84x^169+48x^170+86x^171+48x^172+42x^173+30x^174+6x^176+16x^177+20x^180+6x^183+8x^186+4x^189+6x^192+2x^195+2x^198

The gray image is a linear code over GF(3) with n=711, k=9 and d=432.
This code was found by Heurico 1.16 in 3.04 seconds.