The generator matrix

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

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+9x^26+34x^27+45x^28+28x^29+6x^30+2x^31+2x^32+1x^54

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 0.00545 seconds.