The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3+X^2  1  1  X X^3+X  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 X^3+X X^3+1  0  1 X^2+X X^3+X^2  0
 0  0 X^3  0 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0
 0  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3  0 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+24x^13+66x^14+368x^15+123x^16+352x^17+60x^18+16x^19+4x^20+8x^21+2x^22

The gray image is a linear code over GF(2) with n=128, k=10 and d=52.
This code was found by Heurico 1.16 in 6.87e-008 seconds.