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

generates a code of length 78 over Z3[X]/(X^3) who´s minimum homogenous weight is 148.

Homogenous weight enumerator: w(x)=1x^0+258x^148+80x^150+420x^151+162x^152+160x^153+126x^154+648x^155+3132x^156+156x^157+648x^158+236x^159+180x^160+24x^162+102x^163+60x^166+8x^168+102x^169+2x^171+42x^172+12x^175+2x^225

The gray image is a linear code over GF(3) with n=702, k=8 and d=444.
This code was found by Heurico 1.16 in 38.5 seconds.