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 1 X X 1 1 1 1 1 X 1 1 1 X
0 X 0 0 0 0 0 0 0 0 0 0 0 X X 2X 2X 2X X 2X X X X X 2X X X 0 0 X 0 2X X X X 0 X
0 0 X 0 0 0 0 0 0 0 0 X X 2X X 0 X 2X 2X 2X 0 0 2X X X 0 X X 2X 0 X X 0 X X X 0
0 0 0 X 0 0 0 0 X 2X 2X 2X 2X 2X X 0 X 2X 0 0 0 2X 0 2X 0 X 2X X X 2X X X X 0 0 2X 0
0 0 0 0 X 0 0 X 2X 0 2X 2X X X X 2X X X 0 2X X 2X 2X 2X X 2X 0 X 0 0 2X X 0 2X 2X X X
0 0 0 0 0 X 0 2X 2X X 0 2X 2X X 2X 2X X 2X 2X X 2X X 0 2X X 0 0 2X 0 X 0 0 0 0 0 0 2X
0 0 0 0 0 0 X 2X 2X 2X 2X X 0 X X 0 0 X 2X X X X 2X X 2X 0 2X 0 0 0 2X 2X 0 0 X 2X X
generates a code of length 37 over Z3[X]/(X^2) who´s minimum homogenous weight is 60.
Homogenous weight enumerator: w(x)=1x^0+162x^60+194x^63+18x^64+186x^66+180x^67+286x^69+720x^70+226x^72+1440x^73+250x^75+1440x^76+232x^78+576x^79+270x^81+184x^84+118x^87+38x^90+28x^93+12x^96
The gray image is a linear code over GF(3) with n=111, k=8 and d=60.
This code was found by Heurico 1.16 in 13.9 seconds.