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.