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  X  1  1  1  X  1  1  1  X  1  X  1  1  1  X  1  1
 0  X  0  0  0  0  0  0  0  0  0  0  0 2X  X  X 2X 2X 2X 2X  0  X 2X 2X  X  0  X  X  X  X  X  0  0  X  X 2X  X 2X  X  X  0 2X  X 2X  0  0  0
 0  0  X  0  0  0  0  0  0  0  0  X  X  0  0  X  X 2X  0 2X 2X 2X  X 2X  X  X  X 2X 2X 2X  X  X  X  X 2X  0  0  0  X  X  X  X  0 2X  X  X  0
 0  0  0  X  0  0  0  0  X 2X 2X 2X  X  0  0  0  X  X 2X  0 2X  X  X  X  0  X 2X 2X  0 2X 2X 2X  X 2X  0 2X 2X  0  X  0  0  X 2X  X  X  X  X
 0  0  0  0  X  0  0  X 2X  0 2X  0  X  0 2X  X 2X  X  X  0  0  0  X 2X  X  0  X 2X  0  X 2X 2X 2X 2X  X  X  0 2X  0  0  X  X  X  0 2X 2X  X
 0  0  0  0  0  X  0 2X 2X  X  0 2X  X 2X  0 2X  0  X 2X 2X  0 2X  X  X  0 2X  0  X  0 2X  0  X  X  0 2X  X  0  0 2X  0  X 2X  0  0 2X  X  0
 0  0  0  0  0  0  X 2X 2X 2X 2X 2X 2X  X 2X  X  0  0  X  0  X  X  X  X  X  X 2X  0  X  X  X  X  X  0 2X 2X  X  X  0  X 2X 2X  0 2X  0 2X 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+82x^78+176x^81+6x^82+250x^84+72x^85+216x^87+360x^88+250x^90+960x^91+200x^93+1440x^94+194x^96+1152x^97+180x^99+384x^100+224x^102+174x^105+114x^108+82x^111+34x^114+8x^117+2x^123

The gray image is a linear code over GF(3) with n=141, k=8 and d=78.
This code was found by Heurico 1.16 in 0.849 seconds.