The generator matrix

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

generates a code of length 55 over Z2[X]/(X^2) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+44x^49+55x^50+24x^51+59x^52+52x^53+26x^54+16x^55+30x^56+52x^57+34x^58+24x^59+30x^60+44x^61+6x^62+1x^64+6x^66+6x^68+1x^82+1x^84

The gray image is a linear code over GF(2) with n=110, k=9 and d=49.
This code was found by Heurico 1.16 in 40.8 seconds.