The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 X 1 1 1 1 1 1 1 1 1 X 1
0 X 0 0 0 0 0 0 0 0 0 0 0 2X X X 2X 2X X X 2X 0 X X X X X 2X 2X 2X X 0 0 2X 0 X
0 0 X 0 0 0 0 0 0 0 X X 2X X 2X X 2X 0 X X X X 0 0 2X X 2X 0 2X X 2X X X X X 2X
0 0 0 X 0 0 0 0 X 2X 2X 2X X 0 2X 0 0 X X X 2X X X 0 X 2X X 2X 2X 2X 2X 2X X 0 2X 2X
0 0 0 0 X 0 0 X 2X 0 2X X X 2X 2X X X X 0 X 0 0 X 0 X 0 2X 2X X 0 X 0 2X 2X 2X 2X
0 0 0 0 0 X 0 2X 2X X 2X 2X 0 X 2X 2X 0 X 2X 0 2X 2X X 2X 0 0 X X 2X 0 X 0 0 0 2X 0
0 0 0 0 0 0 X 2X 2X 2X X 0 X 0 2X 2X X 2X 0 0 X 2X 0 0 0 2X X X X 2X 2X X 0 X 2X 2X
generates a code of length 36 over Z3[X]/(X^2) who´s minimum homogenous weight is 57.
Homogenous weight enumerator: w(x)=1x^0+70x^57+188x^60+242x^63+384x^66+1224x^69+2186x^72+1562x^75+258x^78+198x^81+136x^84+58x^87+44x^90+8x^93+2x^99
The gray image is a linear code over GF(3) with n=108, k=8 and d=57.
This code was found by Heurico 1.16 in 0.612 seconds.