The generator matrix

 1  0  0  1  1  1  0  1  1  X  1  1  1  1  1  X  1 X^2+X  1 X^2+X  1  1 X^2 X^2  X  0  X  1
 0  1  0  0  1  1  1 X^2 X^2+X+1  1 X+1  X  X X^2 X+1  1  X  0  1  1 X^2+1 X^2+X  0  0  1  1  1 X^2+1
 0  0  1 X+1 X^2+X+1  0 X+1  X X^2+X X^2+1 X^2+1  1 X^2+X+1 X^2+1 X^2+X+1 X^2+X  X  1 X^2+1  1  X  0  1  1 X^2 X+1  0 X^2+X
 0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2  0  0  0
 0  0  0  0 X^2  0 X^2  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2
 0  0  0  0  0 X^2  0  0  0 X^2  0  0  0 X^2 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 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+587x^24+912x^26+1166x^28+848x^30+527x^32+32x^34+18x^36+5x^40

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 22.9 seconds.