The generator matrix

 1  0  0  1  1  1  0  1 X^2  X  1  1  1  1 X^2+X  X  0  0  1  1  1 X^2+X  X  1  1  1 X^2  1
 0  1  0  0  1 X^2+1  1  X  1  1 X+1  X X+1  1  0  X  1  1 X^2 X^2+X+1 X^2 X^2+X  1 X^2  X X^2+1 X^2+X  0
 0  0  1 X+1 X^2+X+1  0 X+1 X^2+1 X^2+X  1 X^2 X^2+X X+1 X^2+X  1  1 X+1 X^2+1  0 X+1  X  1  X X^2+1  0 X^2  1 X+1
 0  0  0 X^2  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0
 0  0  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0 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+153x^24+184x^25+348x^26+252x^27+359x^28+152x^29+212x^30+128x^31+174x^32+48x^33+28x^34+4x^35+1x^36+4x^38

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 0.0654 seconds.