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

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+582x^151+684x^152+426x^153+1182x^154+564x^155+490x^156+636x^157+444x^158+158x^159+468x^160+330x^161+126x^162+348x^163+72x^164+8x^165+12x^166+6x^167+2x^168+6x^172+6x^175+6x^176+2x^180+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 0.774 seconds.