The generator matrix

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

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+198x^12+128x^13+384x^14+128x^15+175x^16+10x^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 4 seconds.