The generator matrix

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

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+18x^12+76x^13+112x^14+660x^15+315x^16+660x^17+110x^18+76x^19+18x^20+2x^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 6.87e-008 seconds.