The generator matrix

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

generates a code of length 77 over Z3[X]/(X^2) who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+508x^144+1140x^147+1158x^150+1022x^153+804x^156+624x^159+616x^162+336x^165+192x^168+130x^171+24x^174+6x^177

The gray image is a linear code over GF(3) with n=231, k=8 and d=144.
This code was found by Heurico 1.16 in 0.813 seconds.