The generator matrix

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

generates a code of length 47 over Z3[X]/(X^2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+104x^78+266x^81+84x^82+102x^83+594x^84+234x^85+252x^86+874x^87+504x^88+558x^89+1844x^90+768x^91+1038x^92+2032x^93+990x^94+1098x^95+2224x^96+1026x^97+846x^98+1622x^99+552x^100+426x^101+792x^102+180x^103+54x^104+320x^105+36x^106+122x^108+90x^111+42x^114+6x^117+2x^120

The gray image is a linear code over GF(3) with n=141, k=9 and d=78.
This code was found by Heurico 1.16 in 4.49 seconds.