The generator matrix

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

generates a code of length 51 over Z2[X]/(X^2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+12x^54+3x^56

The gray image is a linear code over GF(2) with n=102, k=4 and d=54.
As d=54 is an upper bound for linear (102,4,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 0.0211 seconds.