The generator matrix

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

generates a code of length 78 over Z3[X]/(X^3) who´s minimum homogenous weight is 151.

Homogenous weight enumerator: w(x)=1x^0+468x^151+912x^152+422x^153+966x^154+714x^155+328x^156+666x^157+594x^158+200x^159+378x^160+408x^161+60x^162+246x^163+108x^164+36x^165+18x^166+6x^167+6x^169+12x^173+2x^174+6x^175+2x^177+2x^186

The gray image is a linear code over GF(3) with n=702, k=8 and d=453.
This code was found by Heurico 1.16 in 7.8 seconds.