The generator matrix

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

generates a code of length 55 over Z2[X]/(X^2) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+98x^42+192x^43+358x^44+524x^45+730x^46+872x^47+1070x^48+1322x^49+1498x^50+1842x^51+1966x^52+2124x^53+2344x^54+2426x^55+2451x^56+2326x^57+2122x^58+1970x^59+1640x^60+1356x^61+1110x^62+824x^63+585x^64+358x^65+245x^66+170x^67+116x^68+44x^69+38x^70+22x^71+5x^72+10x^73+4x^74+2x^75+2x^78+1x^82

The gray image is a linear code over GF(2) with n=110, k=15 and d=42.
This code was found by Heurico 1.11 in 43.2 seconds.