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

generates a code of length 82 over Z3[X]/(X^3) who´s minimum homogenous weight is 150.

Homogenous weight enumerator: w(x)=1x^0+34x^150+118x^153+240x^156+280x^159+486x^160+336x^162+1944x^163+528x^165+1944x^166+364x^168+96x^171+84x^174+20x^177+18x^180+10x^183+14x^186+4x^189+16x^192+8x^195+10x^198+4x^201+2x^216

The gray image is a linear code over GF(3) with n=738, k=8 and d=450.
This code was found by Heurico 1.16 in 0.698 seconds.