The generator matrix

 1  1  1  1  1  1  1  1  1  X  1  1  1  X  X  1
 0  X  0 X^3+X^2+X X^2 X^2+X X^3+X^2  X  0 X^3 X^3+X^2+X X^3+X X^2 X^2+X X^3+X^2+X X^2+X
 0  0 X^3+X^2 X^2 X^2  0 X^3 X^2 X^3 X^3+X^2 X^3 X^3 X^3+X^2 X^3 X^2 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+62x^14+76x^15+271x^16+40x^17+33x^18+12x^19+16x^20+1x^26

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 0.016 seconds.