The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  X  X  X  0  0  0  0  0  0  0  1  1  1  1  1  1  1  1  X  X  X  X  X  X  X  X  X  0  0  0  0
 0  X  0  0  0  X  X  X  0  0  0  X  0  X  X  X  0  0  0  X  0  X  X  X  0  0  X  X  0  X  X  X  X  X  X  0  0  0  0  0  0  X  0  X  X  X  0  0  0  X  0  X  X  X  0  X  X  X  X
 0  0  X  0  X  X  X  0  0  0  X  X  X  X  0  0  0  0  X  X  X  X  0  0  0  X  X  0  X  X  0  0  0  X  X  X  X  0  0  0  X  X  X  X  0  0  0  0  X  X  X  X  0  0  0  0  0  X  X
 0  0  0  X  X  0  X  X  0  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0  X  X  0  0  0  X  X  0  X  X  0  0  X  X  0  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0  0  0  X  X  0

generates a code of length 59 over Z2[X]/(X^2) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+24x^60+7x^64

The gray image is a linear code over GF(2) with n=118, k=5 and d=60.
As d=60 is an upper bound for linear (118,5,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 5.
This code was found by Heurico 1.16 in 0.0421 seconds.