The generator matrix

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

generates a code of length 26 over Z3[X]/(X^2) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+498x^41+516x^42+2286x^44+1424x^45+5094x^47+3180x^48+8778x^50+5232x^51+11502x^53+5564x^54+8136x^56+2856x^57+2658x^59+786x^60+414x^62+108x^63+12x^66+4x^72

The gray image is a linear code over GF(3) with n=78, k=10 and d=41.
This code was found by Heurico 1.16 in 755 seconds.