The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  X X^2  X  1  1
 0 X^3+X^2  0  0  0 X^2 X^3+X^2 X^2  0 X^3 X^3 X^2 X^3+X^2 X^2 X^3+X^2  0
 0  0 X^3+X^2  0 X^2 X^2 X^2 X^3  0 X^3  0 X^2  0 X^3+X^2 X^3  0
 0  0  0 X^3+X^2 X^2 X^3 X^3+X^2 X^3+X^2  0 X^3+X^2 X^2  0 X^3  0 X^3  0
 0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  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+94x^12+16x^13+174x^14+368x^15+761x^16+368x^17+156x^18+16x^19+70x^20+22x^22+2x^24

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 0.016 seconds.