The generator matrix

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

generates a code of length 41 over Z3[X]/(X^2) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+104x^66+276x^67+480x^68+1164x^69+1230x^70+1608x^71+3144x^72+2676x^73+3582x^74+6588x^75+6012x^76+7044x^77+11072x^78+9474x^79+10620x^80+15188x^81+11820x^82+11952x^83+16290x^84+10566x^85+10068x^86+11420x^87+6918x^88+5040x^89+5428x^90+2730x^91+1746x^92+1428x^93+696x^94+336x^95+284x^96+90x^97+12x^98+40x^99+14x^102+4x^108+2x^111

The gray image is a linear code over GF(3) with n=123, k=11 and d=66.
This code was found by Heurico 1.16 in 267 seconds.