The generator matrix

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

generates a code of length 14 over Z2[X]/(X^4) who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+120x^11+336x^12+1108x^13+1008x^14+1084x^15+299x^16+108x^17+16x^18+12x^19+4x^20

The gray image is a linear code over GF(2) with n=112, k=12 and d=44.
This code was found by Heurico 1.16 in 0.047 seconds.