The generator matrix

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

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+35x^24+138x^25+341x^26+294x^27+512x^28+274x^29+254x^30+102x^31+58x^32+20x^33+10x^34+4x^35+2x^36+2x^38+1x^42

The gray image is a linear code over GF(2) with n=224, k=11 and d=96.
This code was found by Heurico 1.16 in 0.047 seconds.