The generator matrix

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

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+4x^26+52x^28+4x^30+2x^36+1x^40

The gray image is a linear code over GF(2) with n=112, k=6 and d=52.
This code was found by Heurico 1.16 in 0.00504 seconds.