The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1
 0 X^3  0  0  0  0  0 X^3  0 X^3 X^3  0  0 X^3  0 X^3 X^3
 0  0 X^3  0  0  0 X^3 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3  0
 0  0  0 X^3  0  0 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^3  0
 0  0  0  0 X^3  0 X^3  0 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3
 0  0  0  0  0 X^3 X^3  0 X^3  0 X^3  0  0 X^3 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+16x^14+62x^16+384x^17+32x^18+16x^22+1x^32

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.