The generator matrix

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

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+17x^14+24x^15+85x^16+288x^17+72x^18+8x^20+6x^22+8x^23+2x^24+1x^30

The gray image is a linear code over GF(2) with n=136, k=9 and d=56.
This code was found by Heurico 1.16 in 0.015 seconds.