The generator matrix

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

generates a code of length 55 over Z2[X]/(X^2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+37x^40+128x^41+303x^42+478x^43+702x^44+972x^45+1306x^46+1720x^47+2143x^48+2418x^49+3001x^50+3504x^51+4081x^52+4462x^53+4767x^54+4996x^55+4780x^56+4770x^57+4111x^58+3744x^59+3214x^60+2656x^61+2106x^62+1496x^63+1238x^64+814x^65+563x^66+400x^67+289x^68+150x^69+83x^70+44x^71+25x^72+14x^73+14x^74+2x^75+2x^76+2x^78

The gray image is a linear code over GF(2) with n=110, k=16 and d=40.
This code was found by Heurico 1.11 in 187 seconds.