The generator matrix

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

generates a code of length 54 over Z2[X]/(X^2) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+132x^46+238x^48+278x^50+305x^52+258x^54+266x^56+209x^58+158x^60+112x^62+45x^64+32x^66+9x^68+2x^70+2x^72+1x^74

The gray image is a linear code over GF(2) with n=108, k=11 and d=46.
This code was found by Heurico 1.16 in 13 seconds.