The generator matrix

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

generates a code of length 55 over Z2[X]/(X^3) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+273x^50+399x^52+456x^54+338x^56+316x^58+132x^60+84x^62+21x^64+17x^66+5x^68+4x^70+2x^74

The gray image is a linear code over GF(2) with n=220, k=11 and d=100.
This code was found by Heurico 1.16 in 1.26 seconds.