The generator matrix

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

generates a code of length 29 over Z2[X]/(X^3) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+48x^28+32x^29+40x^30+5x^32+2x^40

The gray image is a linear code over GF(2) with n=116, k=7 and d=56.
As d=57 is an upper bound for linear (116,7,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 7.
This code was found by Heurico 1.16 in 0.00603 seconds.