The generator matrix

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

generates a code of length 29 over Z3[X]/(X^3) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+186x^48+54x^50+600x^51+810x^52+432x^53+3934x^54+4860x^55+1296x^56+13344x^57+9720x^58+1728x^59+13378x^60+6480x^61+864x^62+974x^63+288x^66+58x^69+32x^72+6x^75+4x^78

The gray image is a linear code over GF(3) with n=261, k=10 and d=144.
This code was found by Heurico 1.16 in 66.4 seconds.