The generator matrix

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

generates a code of length 36 over Z3[X]/(X^2) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+144x^61+396x^62+140x^63+726x^64+894x^65+334x^66+1356x^67+1500x^68+390x^69+1644x^70+1686x^71+420x^72+2040x^73+2022x^74+486x^75+1728x^76+1512x^77+288x^78+876x^79+618x^80+92x^81+222x^82+108x^83+24x^84+12x^85+12x^86+6x^87+4x^90+2x^93

The gray image is a linear code over GF(3) with n=108, k=9 and d=61.
This code was found by Heurico 1.16 in 2.69 seconds.