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

generates a code of length 89 over Z3[X]/(X^3) who´s minimum homogenous weight is 171.

Homogenous weight enumerator: w(x)=1x^0+22x^171+42x^174+60x^177+1944x^178+76x^180+30x^183+10x^186+2x^267

The gray image is a linear code over GF(3) with n=801, k=7 and d=513.
This code was found by Heurico 1.16 in 0.357 seconds.