The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3  1  1  1  1  1  1  1
 0  1 X+1 X^2+X X^3+X^2+1  1 X^3+X^2 X+1  1  1 X^3 X^3+X^2+X+1 X^3+X+1 X^2 X^2+X+1 X^2+1
 0  0 X^2  0 X^3+X^2 X^3 X^3  0 X^3+X^2 X^3+X^2 X^2 X^3 X^3+X^2 X^2 X^3  0
 0  0  0 X^3 X^3 X^3  0  0 X^3  0  0 X^3 X^3 X^3  0 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+50x^13+229x^14+432x^15+635x^16+428x^17+215x^18+48x^19+4x^20+2x^21+3x^22+1x^26

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 0.015 seconds.