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

generates a code of length 83 over Z3[X]/(X^3) who´s minimum homogenous weight is 156.

Homogenous weight enumerator: w(x)=1x^0+618x^156+18x^158+1098x^159+162x^160+90x^161+1718x^162+1404x^163+918x^164+2790x^165+2592x^166+1710x^167+2622x^168+1620x^169+180x^170+816x^171+54x^172+504x^174+384x^177+236x^180+84x^183+54x^186+8x^189+2x^225

The gray image is a linear code over GF(3) with n=747, k=9 and d=468.
This code was found by Heurico 1.16 in 47.6 seconds.