The generator matrix

 1  0  0  0  0  1  1  1  1  1  X  1  1  1  0  1  X  1  X  1  1  X  0  1  X  0
 0  1  0  0  0  0 2X+1  1  X X+2  1 2X+2  X X+1  X X+2  1  X  1 2X+1 X+2  0  1 2X+1  1  1
 0  0  1  0  0  0 2X+2  1 2X+1  X  2  2 2X+2  X  1  1  X X+2 2X+2  2 X+1  1 2X+1 2X+1  X X+1
 0  0  0  1  0  1 2X+2  0 X+2 2X  2  1 2X+1 2X+1  0 2X X+1 X+2 X+1 X+1  1 X+1 X+2  0  X  1
 0  0  0  0  1  2 2X+2  0 X+1  1 X+2  X X+1  0 X+2  2 X+2 X+2 2X+2 2X+1 2X+1 X+2  2  2 2X+1  1
 0  0  0  0  0 2X 2X 2X 2X 2X  0 2X  X  0  X  0  X  X 2X  0  0 2X 2X  0  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+256x^39+534x^40+762x^41+1432x^42+2376x^43+2502x^44+4100x^45+6150x^46+6570x^47+9760x^48+13128x^49+12768x^50+15718x^51+19020x^52+15552x^53+15844x^54+15738x^55+10224x^56+9058x^57+7128x^58+3588x^59+2536x^60+1446x^61+522x^62+314x^63+90x^64+24x^66+6x^69

The gray image is a linear code over GF(3) with n=78, k=11 and d=39.
This code was found by Heurico 1.16 in 136 seconds.