The generator matrix

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

generates a code of length 28 over Z2[X]/(X^4) who´s minimum homogenous weight is 25.

Homogenous weight enumerator: w(x)=1x^0+64x^25+114x^26+202x^27+296x^28+186x^29+89x^30+50x^31+6x^32+6x^33+4x^34+4x^35+1x^38+1x^48

The gray image is a linear code over GF(2) with n=224, k=10 and d=100.
This code was found by Heurico 1.16 in 0.015 seconds.