The generator matrix

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

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+322x^44+758x^46+1280x^48+1534x^50+2013x^52+2204x^54+2360x^56+2016x^58+1744x^60+1138x^62+627x^64+274x^66+97x^68+12x^70+2x^72+1x^80+1x^96

The gray image is a linear code over GF(2) with n=110, k=14 and d=44.
This code was found by Heurico 1.16 in 95.7 seconds.