The generator matrix

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

generates a code of length 54 over Z2[X]/(X^2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+62x^52+22x^54+22x^56+8x^58+10x^60+1x^64+2x^70

The gray image is a linear code over GF(2) with n=108, k=7 and d=52.
This code was found by Heurico 1.16 in 0.0223 seconds.