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

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+634x^156+72x^158+1078x^159+108x^160+468x^161+1362x^162+648x^163+1242x^164+3310x^165+2754x^166+1656x^167+2642x^168+864x^169+936x^170+658x^171+490x^174+350x^177+258x^180+102x^183+34x^186+14x^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 18.5 seconds.