The generator matrix

 1  0  0  1  1  1  0  1  1  1 X^3+X X^2+X  1 X^3+X^2  1 X^3  X  1  1  1  1 X^3+X  1  1  0  1  1  1
 0  1  0  0 X^3+X^2+1 X^2+1  1 X^3+X X^3+X+1 X^3  1 X^3  1  1 X^3+X X^3+X^2+X  1 X^3+X^2+X X^3+X^2+1 X^2+X+1 X^3+X^2  1 X^3+X+1 X^3 X^2 X^2+X+1 X^3+X^2+1 X^3+1
 0  0  1 X+1 X+1  0 X^2+X+1 X^3+X^2+X X^3+X+1 X^2+1  1  1  X X^2+X X^2+1  1 X^2+X X^3+X^2  1  0 X^3+X^2+X X^2 X^3+X^2+X X^3+X^2+1  1 X^3+X^2+X+1 X^2 X^3
 0  0  0 X^2 X^3+X^2 X^3 X^2 X^3 X^3+X^2 X^2 X^3+X^2  0 X^3  0  0 X^3 X^2 X^2  0 X^3+X^2 X^3+X^2 X^3 X^2 X^3 X^3+X^2 X^2 X^2 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+405x^24+1036x^25+2204x^26+2736x^27+3543x^28+3048x^29+2144x^30+752x^31+356x^32+108x^33+36x^34+13x^36+2x^40

The gray image is a linear code over GF(2) with n=224, k=14 and d=96.
This code was found by Heurico 1.16 in 2.2 seconds.