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  0  X  X  0  0  0  0  X  0  0
 0  X  0  0  0  0  0  0  0  X  X  X  X  X  X  X  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X
 0  0  X  0  0  0  X  X  X  X  X  0  X  X  0  0  0  0  0  0  X  X  X  X  X  X  X  X  0  0  0  0  0  0  X  X  0  0  X
 0  0  0  X  0  X  X  X  0  0  0  0  X  X  X  X  0  0  X  X  X  X  0  0  0  0  X  X  X  0  X  0  0  X  X  0  0  X  X
 0  0  0  0  X  X  0  X  X  0  X  X  X  0  0  X  0  X  X  0  0  X  X  0  0  X  X  0  0  0  X  X  X  X  0  0  0  0  X

generates a code of length 39 over Z2[X]/(X^2) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+30x^38+30x^40+1x^46+1x^48+1x^62

The gray image is a linear code over GF(2) with n=78, k=6 and d=38.
As d=38 is an upper bound for linear (78,6,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 6.
This code was found by Heurico 1.16 in 7.43 seconds.