The generator matrix

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

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+560x^24+996x^26+1084x^28+888x^30+479x^32+68x^34+20x^36

The gray image is a linear code over GF(2) with n=112, k=12 and d=48.
This code was found by Heurico 1.16 in 1.87 seconds.