The generator matrix

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

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+198x^57+264x^58+576x^59+1152x^60+1728x^61+2004x^62+3212x^63+4134x^64+4434x^65+6226x^66+8700x^67+8202x^68+10650x^69+14016x^70+12114x^71+14352x^72+16206x^73+12618x^74+12260x^75+13050x^76+8268x^77+7702x^78+5694x^79+3432x^80+2608x^81+1530x^82+768x^83+608x^84+288x^85+72x^86+58x^87+12x^90+4x^93+4x^96+2x^99

The gray image is a linear code over GF(3) with n=108, k=11 and d=57.
This code was found by Heurico 1.16 in 222 seconds.