The generator matrix

 1  0  0  0  1  1  1  X  1  1  1  1  1  1 2X  1  1  1  1 2X  0 2X  0  1 2X  1  0  1  1  1  1  1  1  X  0  0  1  1  X  1 2X  1  1  1  0  1  1  1
 0  1  0  0  0 2X 2X  1  1 2X+1 X+2 2X+2  0 2X 2X 2X+1  2  1 2X+2  1  1  1  1 2X+2  1 2X+2  1 X+2 2X X+1 X+1 X+2 X+2  1  1  1  X  1  1  X  1 2X+1 2X+1  2  0  2  X 2X
 0  0  1  0  0 2X+1  2 2X+1  1 2X 2X X+2  1 2X+2  1 2X X+1  2 X+2  X X+2 X+2  2 2X+1  X  1 2X+1 2X+1  1 X+1 2X+2  0 2X+2 2X+2 2X X+2 2X+2  0  X  0  1 2X+1 2X X+1  1  1 X+2  2
 0  0  0  1  1 2X+2  2 X+1  0 X+2 2X+2 2X+1 2X+1  X  2  1  0 X+1  2 X+2 X+2  1 2X  2 2X+1 2X+1  0 X+1 2X 2X+1  X  X  0  2 2X X+2 2X+1  1 X+1 2X+1 X+1 2X+2  2 X+1 X+1 2X  2  0
 0  0  0  0 2X 2X  0  0 2X 2X  0  0  X  X  X  X  X  X  X  0 2X  X 2X  0 2X 2X  X  X  X  0  0  0  X  X  X  0 2X  0  X  X 2X  0 2X  0  X 2X 2X  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+152x^84+198x^85+396x^86+674x^87+726x^88+654x^89+1098x^90+798x^91+876x^92+1246x^93+1020x^94+1176x^95+1568x^96+990x^97+1140x^98+1388x^99+1026x^100+852x^101+1196x^102+672x^103+498x^104+528x^105+336x^106+222x^107+128x^108+66x^109+18x^110+28x^111+2x^114+4x^117+6x^120

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 5.02 seconds.