The generator matrix

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

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+114x^14+64x^15+179x^16+64x^17+68x^18+12x^20+10x^22

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 23.8 seconds.