The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X X^3+X^2  0  1 X^3 X^2  1  1  1  1  X
 0  X  0  X  0 X^3 X^2+X X^2 X^2+X X^2 X^2 X^3+X^2 X^3+X X^3+X^2+X X^2+X  X X^3+X^2  X  X  X X^3+X X^3+X^2 X^2 X^3  0 X^3+X X^3+X^2  X
 0  0  X  X X^3+X^2 X^3+X^2+X X^2+X X^3+X^2 X^3  0  X X^2+X X^2+X  X X^3+X^2 X^2 X^3+X X^3+X X^3+X^2+X X^3+X^2+X  X  X  X X^3+X X^2+X  X X^3+X^2+X  X
 0  0  0 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3  0  0  0  0 X^3  0  0  0 X^3
 0  0  0  0 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3  0 X^3  0  0  0 X^3 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+219x^24+64x^25+764x^26+448x^27+1169x^28+448x^29+680x^30+64x^31+201x^32+28x^34+6x^36+3x^40+1x^44

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 0.625 seconds.