The generator matrix

 1  0  1  1  1  1  1  1 2X^2+X 2X  1  1  1  1  0  1  1 2X^2+X  1  1  1  1  1  1 2X^2 2X^2+2X 2X  1  1  1  1  1  0  1  1 2X^2+X  1  1  1  1  1  1  1  X  1  1  1  0  1  1  X  1  1  1  1 2X^2+X  1  1  1  1  1  1  1 2X^2  1 2X^2+X 2X^2+2X 2X^2+2X  1  1  X  1  1  1  1  0  1
 0  1  1  2 2X^2+X 2X 2X^2+X+2 2X+2  1  1 2X^2+2X+1 X+1 2X^2 2X^2+2  1 2X+1  X  1  2 2X^2+X+1  1 2X^2+2X 2X+2 2X^2+X+2  1  1  1 2X^2+2X+1 2X^2+2X+2 2X^2 X+1 2X^2+2X  1  2 2X  1 2X^2+X+2 X^2+2 2X^2+X X^2 2X+1 X+2 X^2+2  1 X^2+2X+1 2X^2+1 2X^2+X+1  1  0 2X^2+2X+1  1 2X 2X^2+1  1 X^2+2  1 2X^2 2X 2X^2+2X  1 X^2+2 X^2+X  1  1 2X^2+1  1  1  1 2X^2 X^2+X+2  1 X^2+2X 2X^2+1  1 2X+1  X 2X^2+2X+1
 0  0 2X  0  0 X^2 2X^2  0 X^2 X^2 2X^2+2X 2X 2X^2+X  X 2X  X X^2+X X^2+2X X^2+2X 2X^2+X 2X^2+X  X X^2+2X 2X^2+2X  X X^2+X 2X^2+2X X^2+2X 2X^2+X X^2+X 2X^2+2X  X X^2+2X 2X 2X 2X^2 2X^2+2X X^2+2X X^2+2X X^2 X^2+X 2X^2  0  0 X^2+X X^2 X^2+X  0 2X^2+2X X^2 X^2+2X 2X^2 2X 2X 2X^2 X^2 X^2+2X 2X^2+X 2X^2 X^2  X X^2 2X 2X^2  X 2X^2  X 2X X^2 2X^2  X 2X^2+2X 2X^2  X 2X 2X^2+X  0
 0  0  0 X^2  0  0  0 2X^2 X^2 2X^2 2X^2 X^2 X^2 X^2 2X^2 2X^2 2X^2  0 X^2  0 X^2 2X^2 X^2 X^2  0 X^2  0  0 2X^2  0 X^2 X^2 X^2 2X^2  0  0  0  0 X^2 2X^2  0  0 2X^2 X^2 2X^2 X^2 X^2 2X^2 X^2  0 X^2 2X^2  0 X^2 2X^2 2X^2  0 2X^2 X^2 2X^2 2X^2 X^2 X^2 X^2  0 2X^2 X^2 2X^2 X^2 2X^2  0 2X^2 2X^2 2X^2 2X^2  0 2X^2
 0  0  0  0 2X^2 X^2 X^2 2X^2 X^2 2X^2  0  0  0  0 2X^2 X^2 X^2 X^2 2X^2  0 2X^2 2X^2 X^2  0 X^2  0 2X^2 2X^2 2X^2  0 2X^2 2X^2 X^2 X^2  0 2X^2 2X^2  0 2X^2 2X^2 X^2  0 X^2  0 2X^2 2X^2  0 X^2  0 X^2 X^2  0 X^2  0 2X^2  0 X^2  0  0  0  0 2X^2 X^2 X^2 X^2 2X^2 2X^2  0  0 X^2 2X^2 2X^2 2X^2  0 2X^2 X^2  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+696x^144+360x^145+648x^146+2450x^147+1620x^148+2124x^149+4276x^150+3762x^151+4500x^152+5560x^153+5400x^154+6120x^155+5842x^156+4752x^157+3384x^158+3480x^159+1476x^160+684x^161+1056x^162+126x^163+36x^164+340x^165+196x^168+124x^171+26x^174+6x^180+4x^186

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 43.5 seconds.