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

generates a code of length 61 over Z2[X]/(X^2) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+3x^64+8x^65+4x^66

The gray image is a linear code over GF(2) with n=122, k=4 and d=64.
As d=64 is an upper bound for linear (122,4,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 0.045 seconds.