The generator matrix

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

generates a code of length 26 over Z3[X]/(X^2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+114x^40+222x^41+516x^42+864x^43+1002x^44+1494x^45+2130x^46+2244x^47+3144x^48+4194x^49+4074x^50+5254x^51+6366x^52+4860x^53+5348x^54+5400x^55+3732x^56+2984x^57+2334x^58+1194x^59+864x^60+438x^61+168x^62+56x^63+30x^64+10x^66+8x^69+4x^72

The gray image is a linear code over GF(3) with n=78, k=10 and d=40.
This code was found by Heurico 1.16 in 13.8 seconds.