The generator matrix

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

generates a code of length 78 over Z3[X]/(X^2) who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+374x^144+600x^147+744x^150+1196x^153+1002x^156+852x^159+944x^162+498x^165+186x^168+104x^171+6x^174+34x^180+18x^189+2x^198

The gray image is a linear code over GF(3) with n=234, k=8 and d=144.
This code was found by Heurico 1.16 in 17.6 seconds.