The generator matrix

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

generates a code of length 48 over Z3[X]/(X^2) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+510x^84+1494x^87+2524x^90+3068x^93+4080x^96+3576x^99+2772x^102+1254x^105+296x^108+72x^111+24x^114+2x^117+4x^120+6x^123

The gray image is a linear code over GF(3) with n=144, k=9 and d=84.
This code was found by Heurico 1.16 in 53.1 seconds.