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

generates a code of length 48 over Z3[X]/(X^3) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+58x^84+60x^85+90x^86+284x^87+180x^88+192x^89+538x^90+192x^91+672x^92+1654x^93+1656x^94+2202x^95+2748x^96+3192x^97+2268x^98+2116x^99+324x^100+246x^101+398x^102+168x^103+138x^104+110x^105+30x^106+24x^107+44x^108+24x^109+22x^111+6x^112+24x^114+8x^117+10x^120+2x^123+2x^126

The gray image is a linear code over GF(3) with n=432, k=9 and d=252.
This code was found by Heurico 1.16 in 1.59 seconds.