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

generates a code of length 78 over Z3[X]/(X^3) who´s minimum homogenous weight is 142.

Homogenous weight enumerator: w(x)=1x^0+30x^142+96x^143+80x^144+162x^145+258x^146+122x^147+276x^148+348x^149+434x^150+378x^151+894x^152+2040x^153+468x^154+2358x^155+3972x^156+588x^157+2394x^158+2636x^159+534x^160+366x^161+34x^162+258x^163+336x^164+32x^165+108x^166+174x^167+30x^168+78x^169+48x^170+26x^171+30x^172+18x^173+12x^174+20x^177+6x^178+4x^180+14x^183+10x^186+2x^189+6x^192+2x^204

The gray image is a linear code over GF(3) with n=702, k=9 and d=426.
This code was found by Heurico 1.16 in 93.5 seconds.