The generator matrix

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

generates a code of length 28 over Z2[X]/(X^4) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+252x^26+128x^27+359x^28+32x^29+188x^30+32x^31+22x^32+8x^34+1x^36+1x^40

The gray image is a linear code over GF(2) with n=224, k=10 and d=104.
This code was found by Heurico 1.16 in 0.047 seconds.