The generator matrix

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

generates a code of length 17 over Z2[X]/(X^4) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+64x^14+88x^15+168x^16+400x^17+152x^18+88x^19+51x^20+8x^22+3x^24+1x^28

The gray image is a linear code over GF(2) with n=136, k=10 and d=56.
This code was found by Heurico 1.16 in 0.015 seconds.