The generator matrix

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

generates a code of length 62 over Z2[X]/(X^2) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+8x^65+3x^66+3x^68+1x^70

The gray image is a linear code over GF(2) with n=124, k=4 and d=65.
As d=65 is an upper bound for linear (124,4,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 0.0332 seconds.