The generator matrix

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

generates a code of length 16 over Z2[X]/(X^4) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+94x^13+266x^14+370x^15+635x^16+340x^17+236x^18+76x^19+4x^20+14x^21+10x^22+2x^23

The gray image is a linear code over GF(2) with n=128, k=11 and d=52.
This code was found by Heurico 1.16 in 0.062 seconds.