The generator matrix

 1  0  0  1  1  1  1  1  1 2X  1  1  0 2X  1  X  1  1  1  1  1  0  1  1  1 2X  1  1  1  1  1  1  0  X  1 2X  0
 0  1  0  0  0  1  1  2 2X+2  1 2X+1  2  1  1 2X+1  1  1  X  0  2 2X+1  1  0 2X+2 2X+2  1 2X+2  2 2X 2X+1  0 2X  1 2X  X  1  1
 0  0  1  1  2  2  1  0 2X+1 2X+1 2X  2  2  1 X+2  0  1  2  X X+1 2X  1  1  X X+2  0  0  X  X  1 2X+1 X+1 2X  1 2X+2 X+1  2
 0  0  0 2X  0  0  0  0  0  0 2X  X  X  X  X 2X  X  X 2X 2X  X 2X 2X 2X 2X 2X 2X 2X  X 2X  X 2X  X 2X  X  0 2X
 0  0  0  0  X  0 2X 2X  X  X 2X 2X 2X  X 2X  X  X  0  X 2X 2X  X 2X 2X  0 2X  0  X  0  0 2X  X  0  0 2X 2X 2X
 0  0  0  0  0 2X  X 2X  X  0 2X 2X 2X 2X  X  X  0 2X  X  0  0  0  X 2X  0  0  X 2X  X  X  0  0  X 2X  X 2X 2X

generates a code of length 37 over Z3[X]/(X^2) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+66x^62+234x^63+222x^64+540x^65+562x^66+474x^67+954x^68+894x^69+630x^70+1620x^71+1194x^72+870x^73+2022x^74+1506x^75+1050x^76+2076x^77+1312x^78+774x^79+1122x^80+622x^81+312x^82+300x^83+138x^84+42x^85+48x^86+52x^87+26x^90+8x^93+10x^96+2x^99

The gray image is a linear code over GF(3) with n=111, k=9 and d=62.
This code was found by Heurico 1.16 in 4.78 seconds.