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  0  1  1 X^2  1  1  1  X  1  1  X  1  1 X^2  X  1  0
 0  X  0  X  0  0  X X^2+X X^2 X^2  X X^2+X  0 X^2 X^2+X X^2+X  0 X^2  X X^2+X  X  0 X^2 X^2+X  0 X^2  0  X  X  0  X  X  0 X^2 X^2  0  X  0  X X^2+X  0  X X^2 X^2 X^2+X  X X^2 X^2  X  X X^2+X  X X^2+X X^2+X X^2
 0  0  X  X  0 X^2+X  X X^2  0  X  X  0 X^2  X X^2+X X^2  0  X X^2+X  0  0 X^2 X^2+X  X  0  0 X^2+X  X X^2 X^2+X  X X^2  0  X X^2 X^2+X X^2+X  0 X^2  0  X X^2+X  X X^2  X  X X^2+X  0 X^2+X  0  0 X^2 X^2  X  X
 0  0  0 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2  0 X^2 X^2  0
 0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2
 0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0 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+126x^50+8x^51+64x^52+128x^53+113x^54+240x^55+31x^56+128x^57+85x^58+8x^59+27x^60+43x^62+3x^64+17x^66+1x^68+1x^96

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 0.556 seconds.