The generator matrix

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

generates a code of length 36 over Z2[X]/(X^2) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+16x^36+12x^38+3x^40

The gray image is a linear code over GF(2) with n=72, k=5 and d=36.
As d=36 is an upper bound for linear (72,5,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 5.
This code was found by Heurico 1.16 in 0.00698 seconds.