The generator matrix

 1  0  1  1  1  X  1  1 X^2+X  1 X^2  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  1  1 X^2 X+1  1  X X^2+X+1  1 X^2+X  1 X^2+X+1 X^2+X+1 X^2+1  1  1 X^2  0 X^2+X X^2+X  X X^2+1 X^2+1 X^2  0 X^2+X  1 X+1
 0  0  X X^2+X X^2 X^2+X  X X^2+X  0  0  X X^2  X  0 X^2 X^2+X  0 X^2+X X^2+X X^2  0 X^2+X X^2  X X^2  X  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+52x^26+32x^27+92x^28+32x^29+40x^30+2x^32+4x^34+1x^48

The gray image is a linear code over GF(2) with n=112, k=8 and d=52.
This code was found by Heurico 1.16 in 0.00958 seconds.