The generator matrix

 1  1  1  1  1  1  X  0  1  1  X X^3+X^2  X  X X^2 X^2
 0  X X^3+X^2 X^2+X  0 X^2+X X^2+X  X X^3+X^2 X^3+X X^3+X  X X^2+X X^3+X  0  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 X^3 X^3 X^3  0 X^3  0  0  0 X^3 X^3
 0  0  0  0 X^3  0 X^3 X^3  0 X^3  0 X^3  0 X^3  0 X^3
 0  0  0  0  0 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3  0 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+383x^14+256x^15+594x^16+256x^17+371x^18+79x^20+13x^22+1x^24+1x^26

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 0.015 seconds.