The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2+X  1  1  0  1  1 X^2  1  1  X  1  1  1  1 X^2  X  X  X  0  X  X X^2  1  1  1  1  1  1 X^2  1  1
 0  1 X+1 X^2+X X^2+1  1  0 X+1  1 X^2+X X^2+1  1 X^2 X^2+X+1  1  X  1  1 X^2  X X^2+X+1  1  1  1  0 X^2+X  X X^2  X  X  0 X^2+X X^2  X X+1 X^2+1  0 X^2+X+1  1
 0  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0  0 X^2  0  0

generates a code of length 39 over Z2[X]/(X^3) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+61x^38+62x^40+2x^46+1x^48+1x^54

The gray image is a linear code over GF(2) with n=156, k=7 and d=76.
As d=77 is an upper bound for linear (156,7,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 7.
This code was found by Heurico 1.16 in 0.0169 seconds.