The generator matrix

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

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+548x^144+1146x^147+1092x^150+972x^153+798x^156+704x^159+634x^162+356x^165+170x^168+120x^171+2x^174+14x^177+2x^180+2x^183

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 1.91 seconds.