The generator matrix

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

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+624x^78+3540x^81+8900x^84+16164x^87+26806x^90+35484x^93+37862x^96+26632x^99+14872x^102+5068x^105+1032x^108+140x^111+4x^114+12x^117+4x^120+2x^123

The gray image is a linear code over GF(3) with n=141, k=11 and d=78.
This code was found by Heurico 1.16 in 326 seconds.