The generator matrix

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

generates a code of length 69 over Z2[X]/(X^2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+3x^72+8x^73+2x^74+2x^78

The gray image is a linear code over GF(2) with n=138, k=4 and d=72.
As d=72 is an upper bound for linear (138,4,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 0.0717 seconds.