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

generates a code of length 82 over Z3[X]/(X^3) who´s minimum homogenous weight is 153.

Homogenous weight enumerator: w(x)=1x^0+92x^153+402x^154+260x^156+744x^157+398x^159+1608x^160+1354x^162+3870x^163+2916x^164+2282x^165+3774x^166+310x^168+390x^169+128x^171+330x^172+134x^174+252x^175+82x^177+162x^178+52x^180+96x^181+6x^183+36x^184+2x^186+2x^234

The gray image is a linear code over GF(3) with n=738, k=9 and d=459.
This code was found by Heurico 1.16 in 2.86 seconds.