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

generates a code of length 44 over Z3[X]/(X^2) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+138x^69+280x^72+432x^75+548x^78+1170x^81+2810x^84+5000x^87+5118x^90+2452x^93+664x^96+462x^99+328x^102+176x^105+66x^108+26x^111+8x^114+4x^117

The gray image is a linear code over GF(3) with n=132, k=9 and d=69.
This code was found by Heurico 1.16 in 6.77 seconds.