The generator matrix

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

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+1428x^26+1456x^28+1008x^30+175x^32+28x^34

The gray image is a linear code over GF(2) with n=224, k=12 and d=104.
As d=107 is an upper bound for linear (224,12,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 12.
This code was found by Heurico 1.16 in 18.5 seconds.