The generator matrix

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

generates a code of length 39 over Z2[X]/(X^2) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+125x^36+75x^40+47x^44+3x^48+3x^52+1x^56+1x^60

The gray image is a linear code over GF(2) with n=78, k=8 and d=36.
As d=36 is an upper bound for linear (78,8,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 8.
This code was found by Heurico 1.16 in 14 seconds.