The generator matrix

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

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+102x^84+222x^86+308x^87+270x^88+726x^89+1224x^90+2160x^91+2256x^92+5220x^93+6480x^94+3738x^95+9730x^96+8640x^97+3972x^98+6492x^99+4320x^100+1902x^101+716x^102+252x^104+120x^105+54x^107+58x^108+38x^111+28x^114+8x^117+8x^120+2x^123+2x^126

The gray image is a linear code over GF(3) with n=432, k=10 and d=252.
This code was found by Heurico 1.16 in 7.09 seconds.