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

generates a code of length 46 over Z3[X]/(X^2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+100x^72+262x^75+370x^78+446x^81+54x^82+574x^84+540x^85+680x^87+2160x^88+652x^90+4320x^91+762x^93+4320x^94+714x^96+1728x^97+686x^99+514x^102+400x^105+236x^108+100x^111+48x^114+10x^117+2x^120+2x^123+2x^126

The gray image is a linear code over GF(3) with n=138, k=9 and d=72.
This code was found by Heurico 1.16 in 7.14 seconds.