The generator matrix

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

generates a code of length 79 over Z3[X]/(X^2) who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+78x^144+192x^146+186x^147+420x^149+284x^150+450x^152+296x^153+702x^155+224x^156+822x^158+354x^159+672x^161+230x^162+546x^164+216x^165+432x^167+130x^168+120x^170+86x^171+18x^173+36x^174+12x^177+16x^180+18x^183+8x^186+2x^192+4x^195+4x^198+2x^201

The gray image is a linear code over GF(3) with n=237, k=8 and d=144.
This code was found by Heurico 1.16 in 0.96 seconds.