The generator matrix

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

generates a code of length 14 over Z2[X]/(X^4) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+16x^13+28x^14+16x^15+1x^16+2x^20

The gray image is a linear code over GF(2) with n=112, k=6 and d=52.
This code was found by Heurico 1.16 in -6.48e-008 seconds.