The generator matrix

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

generates a code of length 26 over Z3[X]/(X^2) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+132x^36+324x^39+18x^40+446x^42+216x^43+574x^45+1080x^46+850x^48+2880x^49+952x^51+4320x^52+1136x^54+3456x^55+948x^57+1152x^58+648x^60+330x^63+144x^66+58x^69+14x^72+2x^75+2x^78

The gray image is a linear code over GF(3) with n=78, k=9 and d=36.
This code was found by Heurico 1.16 in 2.76 seconds.