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

generates a code of length 90 over Z3[X]/(X^3) who´s minimum homogenous weight is 174.

Homogenous weight enumerator: w(x)=1x^0+36x^174+72x^177+1968x^180+72x^183+36x^186+2x^270

The gray image is a linear code over GF(3) with n=810, k=7 and d=522.
This code was found by Heurico 1.16 in 0.371 seconds.