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

generates a code of length 84 over Z3[X]/(X^3) who´s minimum homogenous weight is 158.

Homogenous weight enumerator: w(x)=1x^0+408x^158+276x^159+18x^160+768x^161+386x^162+90x^163+1518x^164+890x^165+1404x^166+3204x^167+2106x^168+2682x^169+2928x^170+926x^171+180x^172+510x^173+236x^174+300x^176+120x^177+246x^179+90x^180+156x^182+44x^183+120x^185+18x^186+36x^188+8x^189+12x^191+2x^234

The gray image is a linear code over GF(3) with n=756, k=9 and d=474.
This code was found by Heurico 1.16 in 5.76 seconds.