The generator matrix

 1  0  1  1  1 X^2+X  1  1  0  1  1 X^2+X  1  1  0  1  1 X^2+X  1 X^2  1  1  1 X^2+X  1  1  X  1  1  0  1  1  1  1  1  1  0  1 X^2+X  1  1  1  1  X  1  1 X^2+X  X  0  1  1 X^2  1  1  1
 0  1 X+1 X^2+X  1  1  0 X+1  1 X^2+X X^2+1  1  0 X+1  1 X^2+X X^2+1  1 X^2  1 X+1 X^2+1 X^2+X  1 X^2+X+1  X  1  0 X^2+1  1 X^2+1 X^2+1 X+1  1  1  0  1 X^2+X  1  1 X+1 X+1 X^2+X+1 X^2 X^2 X^2+1  1  1  1 X^2+1  X  1 X^2+1 X^2  0
 0  0 X^2  0  0  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2
 0  0  0 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2
 0  0  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2  0
 0  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0 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+65x^50+92x^51+116x^52+124x^53+84x^54+88x^55+82x^56+120x^57+89x^58+76x^59+54x^60+12x^61+16x^62+1x^64+1x^66+1x^74+2x^76

The gray image is a linear code over GF(2) with n=220, k=10 and d=100.
This code was found by Heurico 1.16 in 0.108 seconds.