The generator matrix

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

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+50x^11+284x^12+298x^13+846x^14+222x^15+265x^16+62x^17+10x^18+8x^19+2x^20

The gray image is a linear code over GF(2) with n=112, k=11 and d=44.
This code was found by Heurico 1.16 in 0.047 seconds.