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

generates a code of length 45 over Z3[X]/(X^2) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+76x^66+300x^69+530x^72+6x^74+882x^75+96x^77+1132x^78+672x^80+1432x^81+2688x^83+1762x^84+6720x^86+2148x^87+10752x^89+2520x^90+10752x^92+2442x^93+6144x^95+2156x^96+1536x^98+1690x^99+1266x^102+662x^105+352x^108+206x^111+78x^114+36x^117+8x^120+4x^123

The gray image is a linear code over GF(3) with n=135, k=10 and d=66.
This code was found by Heurico 1.16 in 55.2 seconds.