The generator matrix

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

generates a code of length 16 over Z2[X]/(X^4) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+92x^14+325x^16+92x^18+1x^20+1x^28

The gray image is a linear code over GF(2) with n=128, k=9 and d=56.
This code was found by Heurico 1.16 in 0 seconds.