The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X  1  1  1  1  1  X  1  1  1  1  1  1  1  X  X  1  1  1  1  1  1  1  1  1
 0 X^2  0  0  0  0  0  0  0  0 X^2 2X^2 2X^2 X^2 X^2 X^2  0 2X^2 X^2 2X^2 X^2  0 X^2  0 2X^2 X^2  0 2X^2 X^2 2X^2 2X^2 2X^2 X^2 X^2 X^2  0 2X^2 2X^2  0  0  0 X^2 2X^2 X^2  0 2X^2 X^2 2X^2 X^2 2X^2  0 2X^2 X^2  0 X^2  0 2X^2 X^2 X^2  0  0 2X^2  0 2X^2 2X^2 2X^2 2X^2 X^2  0 X^2 2X^2  0 2X^2 X^2  0 2X^2  0 X^2
 0  0 X^2  0  0  0  0 X^2 2X^2 2X^2 2X^2  0  0 2X^2 X^2 2X^2 X^2  0 X^2 X^2  0 2X^2 2X^2  0 X^2 X^2 2X^2  0 X^2  0 2X^2 2X^2 2X^2 X^2 2X^2  0 2X^2 2X^2 X^2 X^2 2X^2 2X^2 2X^2 2X^2  0  0 2X^2 2X^2  0 X^2 X^2  0 X^2 X^2 X^2 2X^2 2X^2  0 X^2 X^2  0  0 X^2  0 2X^2  0 X^2 2X^2 X^2 2X^2 2X^2  0 X^2 2X^2 2X^2  0 X^2 X^2
 0  0  0 X^2  0  0 X^2 2X^2  0 2X^2  0  0 2X^2 X^2 X^2 2X^2  0 X^2  0 2X^2  0 2X^2 2X^2  0 2X^2  0 X^2 2X^2 2X^2 X^2 X^2 X^2 2X^2  0  0 2X^2 2X^2 X^2 2X^2  0 X^2 2X^2 2X^2 X^2 X^2 2X^2 X^2 2X^2 2X^2  0 2X^2 X^2 2X^2 X^2 2X^2 X^2  0 2X^2 X^2 X^2 X^2  0  0 2X^2 2X^2  0 X^2  0  0 X^2 2X^2  0  0 X^2 2X^2 X^2 X^2 2X^2
 0  0  0  0 X^2  0 2X^2 2X^2 X^2  0 2X^2 2X^2 2X^2  0 2X^2 2X^2  0 2X^2 X^2  0 2X^2 2X^2  0 X^2 2X^2  0 2X^2 X^2  0 X^2  0 X^2  0 2X^2  0 2X^2  0 2X^2 X^2 2X^2  0 X^2 2X^2 X^2 2X^2  0 2X^2 2X^2  0 X^2 2X^2 X^2  0 2X^2 2X^2  0  0 2X^2  0 X^2 X^2 X^2 2X^2  0 2X^2 X^2 X^2 X^2 X^2 2X^2  0 2X^2 2X^2 2X^2 X^2  0 2X^2 X^2
 0  0  0  0  0 X^2 2X^2 2X^2 2X^2 2X^2 2X^2 2X^2 X^2 2X^2 X^2 X^2 2X^2 X^2 2X^2 2X^2 2X^2 2X^2  0 2X^2  0 X^2  0  0 2X^2 X^2 2X^2  0 2X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2 2X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 2X^2 X^2 2X^2 2X^2 X^2 X^2 2X^2  0  0 X^2  0 2X^2 2X^2 X^2 2X^2  0  0 2X^2 2X^2  0 2X^2  0  0  0 X^2 X^2 2X^2

generates a code of length 78 over Z3[X]/(X^3) who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+88x^144+6x^146+114x^147+60x^149+114x^150+240x^152+82x^153+480x^155+4450x^156+480x^158+58x^159+192x^161+42x^162+36x^165+22x^168+18x^171+26x^174+12x^177+12x^180+16x^183+8x^186+2x^195+2x^219

The gray image is a linear code over GF(3) with n=702, k=8 and d=432.
This code was found by Heurico 1.16 in 43.8 seconds.