The generator matrix

 1  0  1  1  1 X^2  1  1  0  1  1  0  X  1  1  1 X^2+X  1  1  1  1  1 X^2+X  1 X^2+X  0  1  1
 0  1  1  0 X+1  1  1  0  1 X^2 X+1  1  1 X^2+1 X^2+X  X  1  1 X^2+X X^2+X+1  0 X^2+X  1 X+1  1  X X^2+X  0
 0  0  X  0  0 X^2  0 X^2+X X^2+X X^2+X X^2+X X^2+X X^2 X^2  0 X^2 X^2+X  X  X  0  0 X^2+X X^2  X  X  X  X  0
 0  0  0  X X^2  X X^2+X X^2+X X^2+X X^2  X X^2 X^2+X X^2  0  X X^2 X^2+X  X X^2+X X^2 X^2 X^2 X^2 X^2+X X^2+X  X  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+84x^24+132x^25+112x^26+160x^27+120x^28+104x^29+132x^30+80x^31+43x^32+20x^33+8x^34+16x^35+8x^36+4x^38

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 0.0245 seconds.