The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1 X^3  1  0  1  1 X^3 X^3+X^2  1  1  X  1  1  X X^2  1
 0  X  0 X^3+X^2+X X^3 X^2+X  0  X X^2 X^3+X^2+X X^3+X^2 X^3+X X^3+X^2  X X^3+X^2  X X^3+X^2+X  X  X  X X^2+X X^3 X^2+X X^2+X X^3 X^2+X X^3 X^3+X^2+X
 0  0 X^3+X^2  0 X^3 X^3+X^2 X^3+X^2 X^2 X^2 X^2 X^3 X^2 X^2 X^3+X^2  0 X^3  0 X^3  0 X^3+X^2  0 X^2 X^3+X^2 X^3+X^2  0 X^3 X^2 X^3
 0  0  0 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^3  0  0 X^3+X^2 X^3+X^2 X^2 X^3 X^3 X^3 X^3 X^2 X^3+X^2 X^2  0 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^3+X^2  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+46x^24+210x^25+235x^26+296x^27+488x^28+342x^29+196x^30+152x^31+37x^32+22x^33+16x^34+4x^36+2x^37+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.