The generator matrix

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

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+6x^74+16x^75+6x^76+2x^78+1x^80

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 0.062 seconds.