The generator matrix

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

generates a code of length 55 over Z2[X]/(X^2) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+48x^44+44x^45+84x^46+152x^47+166x^48+194x^49+222x^50+214x^51+280x^52+276x^53+259x^54+284x^55+232x^56+282x^57+266x^58+248x^59+188x^60+176x^61+147x^62+108x^63+73x^64+50x^65+38x^66+18x^67+28x^68+5x^70+8x^72+2x^73+2x^74+1x^78

The gray image is a linear code over GF(2) with n=110, k=12 and d=44.
This code was found by Heurico 1.16 in 2.05 seconds.