The generator matrix

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

generates a code of length 28 over Z2[X]/(X^3) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+269x^24+448x^26+642x^28+448x^30+207x^32+30x^36+3x^40

The gray image is a linear code over GF(2) with n=112, k=11 and d=48.
This code was found by Heurico 1.16 in 24.3 seconds.