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

generates a code of length 82 over Z3[X]/(X^3) who´s minimum homogenous weight is 157.

Homogenous weight enumerator: w(x)=1x^0+240x^157+348x^158+108x^159+600x^160+300x^161+416x^162+1074x^163+834x^164+554x^165+1050x^166+258x^167+90x^168+300x^169+60x^170+24x^171+60x^172+36x^173+36x^175+72x^176+18x^178+12x^179+18x^180+18x^181+12x^182+6x^184+6x^185+6x^188+2x^192+2x^219

The gray image is a linear code over GF(3) with n=738, k=8 and d=471.
This code was found by Heurico 1.16 in 3.73 seconds.