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

generates a code of length 49 over Z3[X]/(X^3) who´s minimum homogenous weight is 93.

Homogenous weight enumerator: w(x)=1x^0+88x^93+114x^94+108x^95+444x^96+252x^97+736x^99+252x^100+50x^102+12x^103+54x^104+54x^105+18x^106+2x^117+2x^135

The gray image is a linear code over GF(3) with n=441, k=7 and d=279.
This code was found by Heurico 1.16 in 0.0617 seconds.