The generator matrix

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

generates a code of length 28 over Z2[X]/(X^3) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+34x^26+58x^28+28x^30+3x^32+2x^34+2x^36

The gray image is a linear code over GF(2) with n=112, k=7 and d=52.
This code was found by Heurico 1.16 in 0.00717 seconds.