The generator matrix

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

generates a code of length 55 over Z2[X]/(X^2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+123x^52+87x^56+27x^60+10x^64+6x^68+2x^72

The gray image is a linear code over GF(2) with n=110, k=8 and d=52.
As d=52 is an upper bound for linear (110,8,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 8.
This code was found by Heurico 1.16 in 0.0313 seconds.