The generator matrix

 1  0  0  1  1  1  0  1 X^2  1  1  X X^2+X  1  1  X  0  1  1  1 X^2 X^2+X  1  1  X  0  1 X^2+X  1  1  1  X  1  1  1  1  0  1  X X^2  1  0  1 X^2+X  1  1  1  1 X^2+X  1  1  1 X^2  0  1
 0  1  0  0  1 X^2+1  1  X  1  1 X^2+X  1 X^2 X^2+X+1  0  1 X^2+X  1 X^2 X^2+X+1  1  1 X^2+X X^2+X+1  1  1  X  0 X^2+1 X+1 X^2  1 X^2+X X+1 X^2+1  X  1 X^2+X+1  X  1 X^2+1  0 X^2  1  0 X^2+X+1 X+1 X^2+X+1  0 X^2  1  1  1  0  X
 0  0  1 X+1 X^2+X+1  0 X+1 X^2+1 X^2+X  1 X^2 X^2+1  1 X^2  1 X^2+X  1  X X^2+X  1  1 X^2 X^2+X+1 X^2+X  1  1 X+1  1  X X^2+X+1  0 X^2 X+1 X^2+1 X^2+X+1 X^2+1 X^2+X+1  X  1 X^2  X  1  0 X^2 X^2+X+1  1 X+1 X+1  1 X^2+X  1  1 X^2+X  1 X^2+X
 0  0  0 X^2  0  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0
 0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0  0 X^2  0 X^2  0  0  0 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 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+67x^50+248x^51+245x^52+302x^53+204x^54+208x^55+129x^56+176x^57+113x^58+112x^59+82x^60+54x^61+30x^62+32x^63+20x^64+12x^65+2x^66+8x^67+3x^68

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.