The generator matrix

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

generates a code of length 78 over Z3[X]/(X^3) who´s minimum homogenous weight is 150.

Homogenous weight enumerator: w(x)=1x^0+1362x^150+1326x^151+1188x^152+2898x^153+1752x^154+678x^155+2484x^156+1500x^157+726x^158+1904x^159+894x^160+402x^161+1182x^162+594x^163+246x^164+432x^165+90x^166+10x^168+14x^171

The gray image is a linear code over GF(3) with n=702, k=9 and d=450.
This code was found by Heurico 1.16 in 1.47 seconds.