The generator matrix

 1  0  1  1  1  1  1  0  1  0  1  1  1  1  1  0  X  1  1  1  0  1  1  X  1  1  1  1  1  1  0  1  1  1  1  1  1  1  1  1 2X 2X  1  1 2X  1  1  1
 0  1  1  2  0  1  2  1 2X+1  1  0  2 X+2 2X+1  0  1  1  0  2 2X+1  1  2 2X+1  1  X  2 2X+1 2X  X  X  1 2X+2  1 2X 2X+1  1 X+2  1  0  X  1  1 X+1  0  1 2X 2X 2X+1
 0  0 2X  0  0  0  0  0  0  0 2X  X  X 2X 2X 2X 2X 2X 2X  0  X  X  0  0  X 2X  0  X 2X  0 2X 2X  0  X  X  X  X  X 2X 2X 2X  X  X 2X 2X  0  0  0
 0  0  0  X  0  0  0  X 2X  X  0 2X  X 2X 2X  0 2X 2X  0  X 2X  X 2X  X  0 2X  X  X 2X  X  X  0  0  0 2X 2X 2X  0  0  0  X  0 2X  0  0 2X 2X  0
 0  0  0  0  X  0  X  X  X  X  X 2X  0  X  X  0 2X  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X 2X  X  X 2X  0 2X 2X  0  X 2X 2X  X 2X  0 2X  X  X 2X  X
 0  0  0  0  0 2X 2X  0 2X  X  0 2X  X  X 2X 2X  X  X 2X 2X  0  0  X  0  0 2X 2X  X  X  X  0 2X  X  X  X 2X  X  0 2X  X  X  0  0  0 2X  X 2X 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+90x^84+48x^85+60x^86+270x^87+126x^88+144x^89+494x^90+186x^91+228x^92+638x^93+324x^94+306x^95+716x^96+258x^97+372x^98+658x^99+300x^100+258x^101+468x^102+168x^103+66x^104+176x^105+48x^106+24x^107+48x^108+36x^111+26x^114+14x^117+10x^120

The gray image is a linear code over GF(3) with n=144, k=8 and d=84.
This code was found by Heurico 1.16 in 0.533 seconds.