The generator matrix

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

generates a code of length 41 over Z3[X]/(X^2) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+92x^63+288x^66+18x^68+418x^69+36x^71+516x^72+540x^74+578x^75+1800x^77+640x^78+3060x^80+766x^81+4320x^83+852x^84+2556x^86+762x^87+792x^89+658x^90+468x^93+266x^96+150x^99+82x^102+20x^105+4x^108

The gray image is a linear code over GF(3) with n=123, k=9 and d=63.
This code was found by Heurico 1.16 in 6.11 seconds.