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

generates a code of length 91 over Z3[X]/(X^3) who´s minimum homogenous weight is 171.

Homogenous weight enumerator: w(x)=1x^0+244x^171+54x^174+180x^177+618x^180+4374x^182+540x^183+252x^186+172x^189+78x^198+30x^207+16x^216+2x^252

The gray image is a linear code over GF(3) with n=819, k=8 and d=513.
This code was found by Heurico 1.16 in 58 seconds.