The generator matrix

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

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+94x^50+190x^51+228x^52+290x^53+286x^54+212x^55+165x^56+144x^57+108x^58+100x^59+56x^60+50x^61+43x^62+20x^63+28x^64+12x^65+12x^66+6x^67+2x^68+1x^70

The gray image is a linear code over GF(2) with n=220, k=11 and d=100.
This code was found by Heurico 1.11 in 0.11 seconds.