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

generates a code of length 49 over Z3[X]/(X^2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+120x^78+274x^81+404x^84+450x^87+740x^90+1952x^93+4488x^96+5902x^99+3274x^102+730x^105+528x^108+362x^111+244x^114+134x^117+56x^120+16x^123+6x^126+2x^135

The gray image is a linear code over GF(3) with n=147, k=9 and d=78.
This code was found by Heurico 1.16 in 7.92 seconds.