The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 0 0 1 X 2X 0 1 X
0 1 1 2 0 1 2 1 0 2X+1 2 1 0 2X+1 2 1 0 2X+1 1 1 0 1 1 1 2X+1 1
0 0 2X 0 0 0 0 0 0 2X X 2X X X 0 X X 0 X 2X 0 X X 2X 2X X
0 0 0 X 0 0 0 0 0 0 0 0 0 0 X 2X 2X X X X 2X X 2X X X 0
0 0 0 0 X 0 0 0 0 0 0 0 2X 2X 2X 2X 0 X 2X 2X 2X X 0 0 2X X
0 0 0 0 0 2X 0 0 X 2X 2X X X 0 0 X 0 2X X 0 X 0 2X 2X 2X X
0 0 0 0 0 0 X 0 X 0 X X 2X X 2X X X X X 2X 2X 2X X X 0 2X
0 0 0 0 0 0 0 X X X X 0 X 2X 0 0 0 0 X 2X 2X 2X X 0 2X 0
generates a code of length 26 over Z3[X]/(X^2) who´s minimum homogenous weight is 36.
Homogenous weight enumerator: w(x)=1x^0+132x^36+42x^38+336x^39+36x^40+228x^41+410x^42+432x^43+918x^44+598x^45+2160x^46+3066x^47+836x^48+5760x^49+6798x^50+1014x^51+8640x^52+8712x^53+1088x^54+6912x^55+5154x^56+942x^57+2304x^58+1074x^59+630x^60+252x^62+354x^63+150x^66+52x^69+14x^72+4x^75
The gray image is a linear code over GF(3) with n=78, k=10 and d=36.
This code was found by Heurico 1.16 in 24.9 seconds.