The generator matrix

 1  0  1  1  1  0  1  1  0  1  0  1  1  1  1  X  1  1  0  1  1  1  0  1  X  1  1  1  1  0  1  1  X  1  X  X  1  X  1  1  0  1  X  0  X  X  X  0  1  1  0  0  1  1  1
 0  1  1  0  1  1  0 X+1  1  0  1 X+1 X+1 X+1  X  1 X+1  0  1 X+1  1  0  1  X  1 X+1  1  0  1  1  1  X  1  X  1  0  1  X X+1  1  X  X  1  0  0  0  0  X  0  X  1  1  X  0  0
 0  0  X  0  0  0  0  0  X  X  0  X  X  0  X  X  0  X  X  X  X  0  0  X  X  0  X  X  X  X  0  X  X  0  0  0  0  X  0  X  0  0  0  X  0  X  0  X  X  0  X  X  X  0  0
 0  0  0  X  0  0  0  0  X  X  X  0  0  X  0  0  X  0  0  X  X  X  X  X  X  0  0  X  0  X  0  0  0  X  X  X  X  X  0  X  X  0  0  X  0  0  0  0  0  X  0  X  X  0  0
 0  0  0  0  X  0  0  X  0  0  0  X  X  X  0  0  X  0  0  X  X  0  0  0  0  X  X  0  X  0  X  0  0  0  0  X  X  X  0  X  X  0  0  X  X  X  X  X  0  X  0  X  0  X  0
 0  0  0  0  0  X  X  X  X  0  X  0  X  0  0  0  X  X  X  X  0  X  0  X  0  0  X  X  0  0  X  X  X  X  0  0  0  X  X  X  0  X  X  X  X  0  0  X  0  0  0  X  0  0  0

generates a code of length 55 over Z2[X]/(X^2) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+23x^50+32x^51+16x^52+20x^53+22x^54+40x^55+30x^56+8x^57+16x^58+16x^59+14x^60+4x^61+2x^62+8x^63+1x^64+1x^66+1x^68+1x^100

The gray image is a linear code over GF(2) with n=110, k=8 and d=50.
This code was found by Heurico 1.16 in 0.032 seconds.