The generator matrix

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

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+107x^24+272x^26+275x^28+272x^30+84x^32+9x^36+4x^40

The gray image is a linear code over GF(2) with n=112, k=10 and d=48.
This code was found by Heurico 1.16 in 0.0253 seconds.