The generator matrix

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

generates a code of length 55 over Z2[X]/(X^2) who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+62x^43+144x^44+278x^45+367x^46+468x^47+645x^48+732x^49+833x^50+916x^51+940x^52+1036x^53+1171x^54+1166x^55+1144x^56+1108x^57+974x^58+962x^59+873x^60+682x^61+623x^62+428x^63+306x^64+240x^65+111x^66+92x^67+42x^68+20x^69+15x^70+2x^71+2x^74+1x^92

The gray image is a linear code over GF(2) with n=110, k=14 and d=43.
This code was found by Heurico 1.16 in 56.4 seconds.