The generator matrix

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

generates a code of length 36 over Z3[X]/(X^3) who�s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+292x^63+126x^64+288x^65+1680x^66+1224x^67+2250x^68+5176x^69+5292x^70+7074x^71+9196x^72+8568x^73+7110x^74+6478x^75+2286x^76+774x^77+814x^78+366x^81+46x^84+4x^87+4x^93

The gray image is a linear code over GF(3) with n=324, k=10 and d=189.
This code was found by Heurico 1.16 in 4.76 seconds.