The generator matrix

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

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+74x^25+52x^26+174x^27+484x^28+136x^29+24x^30+32x^31+11x^32+30x^33+3x^34+2x^35+1x^50

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 0.109 seconds.