The generator matrix

 1  0  0  1  1  1 X^3+X  1  1 X^3+X^2  1 X^2+X  1  1
 0  1  0 X^2  1 X^3+X+1  1 X^3+X X^3+X^2+1  1  0  1  1 X^3+X
 0  0  1 X^2+X+1  1 X^2 X^2+1 X^2+1  X X+1 X^2+X X^2+X X^2+X+1 X^3+1
 0  0  0 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3  0 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+210x^11+880x^12+1458x^13+3128x^14+1452x^15+827x^16+204x^17+24x^18+2x^19+4x^20+2x^21

The gray image is a linear code over GF(2) with n=112, k=13 and d=44.
This code was found by Heurico 1.16 in 0.171 seconds.