The generator matrix

 1  0  1  1  1 X^3+X^2+X  1  1  X  1  1 X^2+X  1  1 X^3+X^2  1  1 X^3  1  1  1  1 X^3 X^2+X  X  1  1  0
 0  1 X+1 X^2+X X^2+1  1 X^3+X^2+X X^2+X+1  1  X X+1  1 X^3+X^2 X^3+1  1 X^3 X^3+X^2+1  1 X^3+X X^2 X+1 X^3+X^2+1  1  1 X^3 X^3+X^2+X+1 X^3+X^2+X+1  X
 0  0 X^2  0 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^2 X^3  0  0 X^3  0 X^2 X^3+X^2 X^2 X^3 X^2  0 X^3+X^2 X^2 X^3 X^2 X^3 X^2 X^3+X^2
 0  0  0 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0 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+172x^25+232x^26+500x^27+314x^28+448x^29+200x^30+128x^31+19x^32+20x^33+12x^35+2x^36

The gray image is a linear code over GF(2) with n=224, k=11 and d=100.
This code was found by Heurico 1.16 in 0.031 seconds.