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

generates a code of length 49 over Z3[X]/(X^3) who´s minimum homogenous weight is 91.

Homogenous weight enumerator: w(x)=1x^0+174x^91+174x^92+60x^93+216x^94+402x^95+1046x^96+216x^97+1398x^98+1976x^99+114x^100+294x^101+44x^102+90x^103+66x^104+16x^105+72x^106+60x^107+12x^108+72x^109+36x^110+2x^111+18x^112+2x^138

The gray image is a linear code over GF(3) with n=441, k=8 and d=273.
This code was found by Heurico 1.16 in 0.221 seconds.