The generator matrix
1 0 0 1 1 1 1 1 0 1 1 1 2X 1 1 1 1 1 0 2X 1 1 1 1 1
0 1 0 1 0 2 1 2 1 0 2X+1 2X+2 1 2X 2 1 0 X+1 0 1 2X 2X+1 2X 2X+1 0
0 0 1 2 1 2 1 0 2 2 2X 2X+1 2X+1 2X+1 X 1 2 2 1 1 2X+2 0 2X+2 X+2 0
0 0 0 2X 0 0 0 0 0 0 2X X X X 2X 2X 2X X X 0 X 0 2X 0 0
0 0 0 0 2X 0 0 0 X X 2X 2X X 2X 2X 0 X 2X X X X X X 0 X
0 0 0 0 0 X 0 X X 0 X 2X 2X 2X 0 0 2X X 0 2X 0 X X 0 X
0 0 0 0 0 0 X 2X X X 2X 0 X 2X X 2X 0 0 X 0 0 2X 2X 0 X
generates a code of length 25 over Z3[X]/(X^2) who´s minimum homogenous weight is 36.
Homogenous weight enumerator: w(x)=1x^0+100x^36+210x^38+330x^39+1128x^41+850x^42+3456x^44+2620x^45+8508x^47+4778x^48+11658x^50+5362x^51+9720x^53+3876x^54+4134x^56+1462x^57+552x^59+208x^60+72x^63+16x^66+6x^69+2x^75
The gray image is a linear code over GF(3) with n=75, k=10 and d=36.
This code was found by Heurico 1.16 in 11.2 seconds.