The generator matrix

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

generates a code of length 39 over Z3[X]/(X^2) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+300x^63+396x^64+768x^65+1604x^66+1416x^67+2370x^68+3888x^69+3408x^70+4380x^71+7932x^72+7236x^73+7968x^74+12818x^75+10884x^76+11832x^77+16640x^78+12468x^79+12222x^80+15360x^81+9708x^82+7998x^83+9076x^84+5184x^85+3726x^86+3596x^87+1512x^88+1110x^89+834x^90+264x^91+114x^92+98x^93+12x^94+14x^96+6x^99+2x^102+2x^108

The gray image is a linear code over GF(3) with n=117, k=11 and d=63.
This code was found by Heurico 1.16 in 250 seconds.