The generator matrix

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

generates a code of length 14 over Z2[X]/(X^4) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+108x^12+280x^13+300x^14+208x^15+95x^16+24x^17+4x^18+4x^20

The gray image is a linear code over GF(2) with n=112, k=10 and d=48.
This code was found by Heurico 1.16 in 0.016 seconds.