The generator matrix

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

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+40x^50+304x^51+148x^52+384x^53+122x^54+348x^55+83x^56+228x^57+22x^58+150x^59+42x^60+56x^61+29x^62+40x^63+14x^64+20x^65+8x^66+6x^67+3x^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 1.16 in 0.199 seconds.