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

generates a code of length 73 over Z2[X]/(X^2) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+22x^74+4x^76+1x^78+3x^80+1x^86

The gray image is a linear code over GF(2) with n=146, k=5 and d=74.
As d=74 is an upper bound for linear (146,5,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 5.
This code was found by Heurico 1.16 in 0.104 seconds.