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

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+204x^52+360x^53+122x^54+540x^55+558x^56+164x^57+576x^58+624x^59+204x^60+690x^61+726x^62+84x^63+594x^64+432x^65+122x^66+234x^67+204x^68+30x^69+78x^70+12x^71+2x^75

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 12.4 seconds.