The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  1 X^3  X  1  1  X  1  1 X^3+X^2 X^3  1  1  X  1 X^2
 0  X  0 X^3+X^2+X X^2 X^2+X X^3+X^2  X X^3  0 X^2 X^2 X^2+X X^2+X  X X^3+X^2+X X^3+X^2+X X^3+X^2+X X^2+X  X X^3  X  X X^3+X^2 X^3+X^2 X^2  0 X^3+X^2
 0  0 X^3+X^2  0 X^2  0  0 X^3  0 X^2 X^2 X^3 X^3 X^3+X^2 X^3+X^2  0 X^2 X^3+X^2 X^3+X^2 X^2 X^3 X^3 X^3  0 X^2 X^3 X^3+X^2 X^3
 0  0  0 X^3+X^2  0  0 X^3 X^2 X^2 X^2 X^3+X^2 X^2 X^3 X^3+X^2 X^3 X^2  0 X^2 X^2 X^2 X^2 X^3 X^3+X^2 X^3 X^2 X^3+X^2 X^2 X^3
 0  0  0  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3  0 X^3 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+305x^24+64x^25+658x^26+448x^27+1189x^28+448x^29+652x^30+64x^31+204x^32+34x^34+27x^36+2x^40

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 49.2 seconds.