The generator matrix

 1  0  0  1  1  1 X^2+X  X  1  1 X^2+X  X  1  1  1 X^2+X  1  1 X^2  1  0  1 X^2+X  1  1  1  X X^2
 0  1  0  0 X^2+1 X+1  1 X^2  0 X^2+X+1  1  1  X X+1 X+1  1 X^2  1  1 X^2+1 X^2+X X^2+X  1  X  0 X^2+X+1  0  1
 0  0  1  1 X^2+1  0 X^2+1  1 X^2 X^2+X+1  0 X+1  1  X  X X+1 X^2+X+1 X^2 X^2+X+1  1  1  X  X X+1 X^2+1  1  1 X^2+1
 0  0  0  X  X X^2 X^2+X  X X^2+X X^2  X X^2+X X^2 X^2+X  0 X^2  X X^2 X^2+X  0  X  X  0 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+175x^24+188x^25+326x^26+200x^27+337x^28+224x^29+246x^30+120x^31+154x^32+36x^33+34x^34+3x^36+2x^38+2x^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 0.0646 seconds.