The generator matrix

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

generates a code of length 16 over Z2[X]/(X^4) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+93x^12+320x^14+1225x^16+320x^18+82x^20+6x^24+1x^28

The gray image is a linear code over GF(2) with n=128, k=11 and d=48.
This code was found by Heurico 1.16 in 2.13 seconds.