The generator matrix

 1  0  1  1 X^2+X  1  1  1  0  1  1  X  1  1 X^3+X  1  1 X^3+X^2  0  1 X^3+X^2+X X^3+X^2 X^3  0  X  X  1  1
 0  1  1 X^2+X  1 X^3+X+1 X^3+X^2+1 X^2  1  X X^3+X^2+X+1  1 X^2  1  1 X^2+X+1 X^3+X  1  1 X^2+X+1  1  X  1  1  0  0 X^2+1  0
 0  0  X  0 X^3 X^2 X^3+X^2 X^3+X X^3+X^2+X  X X^3+X^2+X X^3+X X^3+X^2+X X^2+X X^2+X  X X^3+X^2+X X^3+X^2+X X^3 X^2 X^3+X^2+X X^3+X X^2  X X^3+X X^3+X^2  0  0
 0  0  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3  0  0  0 X^3 X^3  0  0 X^3  0 X^3 X^3  0 X^3

generates a code of length 28 over Z2[X]/(X^4) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+41x^24+354x^25+417x^26+1050x^27+541x^28+952x^29+323x^30+268x^31+70x^32+50x^33+11x^34+10x^35+3x^36+4x^37+1x^38

The gray image is a linear code over GF(2) with n=224, k=12 and d=96.
This code was found by Heurico 1.16 in 0.078 seconds.