The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  0  1  1 X^2  1 X^2  1  1 X^2  1
 0  X  0  0  0  X X^2+X  X  0 X^2  X X^2+X  0 X^2  X  X  0 X^2  X  X X^2+X X^2 X^2+X  0 X^2+X  X X^2  0 X^2 X^2+X  X  0 X^2 X^2 X^2 X^2 X^2+X  X  X  X X^2+X  0 X^2  0  0 X^2  0 X^2+X  X  0  X  X X^2+X  0  0
 0  0  X  0  X  X  X X^2  0 X^2 X^2+X X^2+X  X  X X^2 X^2  0 X^2+X  0  X  X  X  0  0 X^2+X X^2+X X^2+X X^2  0 X^2  0  X  X X^2+X X^2 X^2 X^2 X^2  X X^2+X X^2 X^2+X X^2 X^2 X^2  X X^2 X^2 X^2+X  X X^2+X  X X^2+X  X X^2
 0  0  0  X  X X^2 X^2+X X^2+X  0 X^2+X X^2 X^2+X  X  0  X  0 X^2 X^2+X X^2+X  0 X^2+X X^2  0 X^2+X  0  X  X X^2 X^2+X X^2+X  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0  X X^2+X X^2+X X^2+X X^2+X X^2  X X^2+X X^2  0 X^2 X^2+X X^2+X X^2+X X^2
 0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  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+134x^50+12x^51+55x^52+112x^53+84x^54+264x^55+50x^56+112x^57+108x^58+12x^59+16x^60+52x^62+5x^64+6x^66+1x^100

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 9.26 seconds.