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

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+62x^84+92x^87+126x^90+110x^93+486x^94+60x^96+972x^97+70x^99+50x^102+42x^105+36x^108+42x^111+20x^114+10x^117+6x^120+2x^141

The gray image is a linear code over GF(3) with n=144, k=7 and d=84.
This code was found by Heurico 1.16 in 0.134 seconds.