The generator matrix

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

generates a code of length 28 over Z3[X]/(X^3) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+198x^49+756x^50+1770x^51+3066x^52+3672x^53+6378x^54+7374x^55+8676x^56+10798x^57+7722x^58+4590x^59+2638x^60+1020x^61+270x^62+38x^63+60x^64+18x^65+2x^66+2x^69

The gray image is a linear code over GF(3) with n=252, k=10 and d=147.
This code was found by Heurico 1.16 in 2.74 seconds.