The generator matrix

 1  0  0  1  1  1  0  X  1  1  1  1  X  X  1 X^2  0  1  1  1  1  1  1  1  X  1  1  1
 0  1  0  0  1  1  1 X^2 X^2+1  X X^2+X X+1  1  1 X^2+1  1  1 X+1  1 X^2+X+1 X^2  X X^2 X^2+X  1 X^2+1 X^2+X  0
 0  0  1  1 X^2 X^2+1  1  1  X  0 X+1 X^2+1  1  0  X  1 X+1  X X^2+X+1 X+1 X^2  1  1 X+1  X X+1  X  0
 0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0  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+42x^24+134x^25+153x^26+194x^27+96x^28+124x^29+93x^30+88x^31+35x^32+22x^33+25x^34+14x^35+2x^36+1x^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 1.11 in 1.05e-007 seconds.