The generator matrix

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

generates a code of length 55 over Z2[X]/(X^2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+12x^54+32x^55+14x^56+2x^62+1x^64+2x^70

The gray image is a linear code over GF(2) with n=110, k=6 and d=54.
This code was found by Heurico 1.16 in 0.0208 seconds.