The generator matrix

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

generates a code of length 58 over Z2[X]/(X^2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+178x^56+32x^60+35x^64+10x^72

The gray image is a linear code over GF(2) with n=116, k=8 and d=56.
As d=56 is an upper bound for linear (116,8,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 8.
This code was found by Heurico 1.16 in 70.7 seconds.