The generator matrix

 1  0  1  1  1 X^2+X  1  1  1  1 X^3+X^2 X^3+X  1  1  1  1
 0  1 X+1 X^2+X X^2+1  1 X^3+X^2 X^3+X X^3+X^2+X+1 X^3+1  1  1  0 X^2+X X^3+X^2 X^3
 0  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0 X^3  0  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+36x^14+176x^15+85x^16+176x^17+36x^18+2x^24

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.