The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 X X^2 X X X
0 X^3+X^2 0 X^2 0 X^3 X^3+X^2 X^3+X^2 0 X^3 0 0 X^2 X^2 X^3 X^3+X^2 X^3+X^2
0 0 X^3+X^2 X^2 0 X^2 X^2 X^3 0 X^2 X^3 X^2 X^2 X^3+X^2 X^3 0 0
0 0 0 X^3 0 0 X^3 0 X^3 X^3 X^3 X^3 0 X^3 X^3 0 X^3
0 0 0 0 X^3 X^3 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+100x^14+285x^16+256x^17+312x^18+32x^20+36x^22+2x^24
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 3.75 seconds.