The generator matrix

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

generates a code of length 26 over Z3[X]/(X^2) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+208x^39+60x^40+78x^41+858x^42+456x^43+540x^44+2338x^45+1224x^46+1692x^47+5370x^48+2544x^49+3282x^50+8556x^51+4110x^52+4050x^53+8738x^54+3096x^55+2736x^56+4890x^57+1392x^58+744x^59+1590x^60+240x^61+180x^63+62x^66+12x^69+2x^72

The gray image is a linear code over GF(3) with n=78, k=10 and d=39.
This code was found by Heurico 1.16 in 37.7 seconds.