The generator matrix

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

generates a code of length 77 over Z3[X]/(X^3) who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+608x^144+180x^145+738x^146+2094x^147+2178x^148+2430x^149+3954x^150+3798x^151+4734x^152+4552x^153+5850x^154+6444x^155+5616x^156+5328x^157+3726x^158+2808x^159+1494x^160+882x^161+794x^162+126x^163+336x^165+234x^168+94x^171+36x^174+6x^177+8x^180

The gray image is a linear code over GF(3) with n=693, k=10 and d=432.
This code was found by Heurico 1.16 in 16.8 seconds.