The generator matrix

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

generates a code of length 54 over Z2[X]/(X^2) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+26x^44+86x^45+148x^46+196x^47+216x^48+244x^49+261x^50+258x^51+254x^52+238x^53+285x^54+278x^55+266x^56+278x^57+211x^58+214x^59+183x^60+132x^61+91x^62+70x^63+72x^64+38x^65+28x^66+8x^67+5x^68+8x^69+1x^72

The gray image is a linear code over GF(2) with n=108, k=12 and d=44.
This code was found by Heurico 1.16 in 1.73 seconds.