The generator matrix

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

generates a code of length 49 over Z3[X]/(X^3) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+270x^88+660x^89+1678x^90+2994x^91+4968x^92+6692x^93+9042x^94+12744x^95+16196x^96+16704x^97+23370x^98+22700x^99+18654x^100+16686x^101+11048x^102+6390x^103+3510x^104+1564x^105+756x^106+156x^107+104x^108+96x^109+90x^110+38x^111+12x^112+18x^113+6x^116

The gray image is a linear code over GF(3) with n=441, k=11 and d=264.
This code was found by Heurico 1.16 in 46.6 seconds.