The generator matrix

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

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+54x^39+54x^40+210x^41+582x^42+690x^43+936x^44+1872x^45+1770x^46+2208x^47+3918x^48+3498x^49+4092x^50+6324x^51+4836x^52+5088x^53+6268x^54+4332x^55+3732x^56+3906x^57+1956x^58+1098x^59+990x^60+360x^61+132x^62+110x^63+24x^66+6x^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 13 seconds.