The generator matrix

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

generates a code of length 30 over Z3[X]/(X^2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+192x^52+354x^53+126x^54+480x^55+636x^56+154x^57+642x^58+612x^59+178x^60+780x^61+618x^62+134x^63+492x^64+408x^65+116x^66+276x^67+270x^68+20x^69+54x^70+18x^71

The gray image is a linear code over GF(3) with n=90, k=8 and d=52.
This code was found by Heurico 1.16 in 10.7 seconds.