The generator matrix

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

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+5x^12+58x^13+7x^14+44x^15+2x^16+10x^17+1x^18

The gray image is a linear code over GF(2) with n=112, k=7 and d=48.
This code was found by Heurico 1.16 in 6.87e-008 seconds.