The generator matrix

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

generates a code of length 55 over Z2[X]/(X^2) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+44x^53+24x^54+28x^56+16x^57+8x^58+3x^64+4x^69

The gray image is a linear code over GF(2) with n=110, k=7 and d=53.
This code was found by Heurico 1.16 in 2.07 seconds.