The generator matrix

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

generates a code of length 81 over Z3[X]/(X^3) who´s minimum homogenous weight is 156.

Homogenous weight enumerator: w(x)=1x^0+186x^156+270x^157+1068x^158+586x^159+540x^160+948x^161+312x^162+162x^163+630x^164+288x^165+378x^166+696x^167+306x^168+108x^169+60x^170+12x^171+4x^174+2x^189+2x^192+2x^195

The gray image is a linear code over GF(3) with n=729, k=8 and d=468.
This code was found by Heurico 1.16 in 0.363 seconds.