The generator matrix

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

generates a code of length 58 over Z2[X]/(X^2) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+8x^61+4x^62+3x^64

The gray image is a linear code over GF(2) with n=116, k=4 and d=61.
As d=61 is an upper bound for linear (116,4,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 0.476 seconds.