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

generates a code of length 81 over Z3[X]/(X^3) who´s minimum homogenous weight is 150.

Homogenous weight enumerator: w(x)=1x^0+104x^150+18x^152+116x^153+120x^155+74x^156+264x^158+112x^159+354x^161+4436x^162+420x^164+52x^165+222x^167+56x^168+60x^170+28x^171+26x^174+28x^177+24x^180+6x^183+16x^186+8x^189+2x^192+6x^195+4x^198+2x^204+2x^219

The gray image is a linear code over GF(3) with n=729, k=8 and d=450.
This code was found by Heurico 1.16 in 0.692 seconds.