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

generates a code of length 84 over Z3[X]/(X^3) who´s minimum homogenous weight is 161.

Homogenous weight enumerator: w(x)=1x^0+330x^161+220x^162+126x^163+552x^164+514x^165+432x^166+846x^167+808x^168+702x^169+756x^170+504x^171+198x^172+174x^173+56x^174+90x^176+32x^177+90x^179+12x^180+30x^182+24x^183+36x^185+6x^186+12x^188+8x^189+2x^225

The gray image is a linear code over GF(3) with n=756, k=8 and d=483.
This code was found by Heurico 1.16 in 18.1 seconds.