The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3+X^2  1  1 X^3+X  X  X  X  0  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  1  0  0 X^2+X  X X^3
 0  0 X^3  0 X^3  0  0 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3
 0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3 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+36x^14+112x^15+282x^16+168x^17+284x^18+96x^19+36x^20+8x^21+1x^32

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 6.87e-008 seconds.