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

generates a code of length 48 over Z3[X]/(X^3) who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+48x^87+42x^88+84x^89+148x^90+144x^91+132x^92+138x^93+54x^94+84x^95+4972x^96+96x^97+54x^98+110x^99+54x^100+42x^101+74x^102+54x^103+42x^104+72x^105+24x^106+42x^107+18x^108+18x^109+6x^110+4x^111+2x^114+2x^144

The gray image is a linear code over GF(3) with n=432, k=8 and d=261.
This code was found by Heurico 1.16 in 0.217 seconds.