The generator matrix

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

generates a code of length 30 over Z3[X]/(X^2) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+90x^39+270x^42+606x^45+968x^48+1338x^51+486x^52+2038x^54+3888x^55+2772x^57+11664x^58+3064x^60+15552x^61+2946x^63+7776x^64+2334x^66+1632x^69+924x^72+460x^75+174x^78+46x^81+18x^84+2x^87

The gray image is a linear code over GF(3) with n=90, k=10 and d=39.
This code was found by Heurico 1.16 in 25.5 seconds.