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

generates a code of length 82 over Z3[X]/(X^3) who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+44x^144+114x^147+232x^150+260x^153+548x^156+724x^159+1152x^162+13122x^164+1334x^165+1002x^168+528x^171+180x^174+118x^177+88x^180+56x^183+76x^186+54x^189+32x^192+8x^195+4x^198+4x^201+2x^216

The gray image is a linear code over GF(3) with n=738, k=9 and d=432.
This code was found by Heurico 1.16 in 4.5 seconds.