The generator matrix

 1  1  1  1  1  1  1  1  X  1 X^3  X  1  1  1  X  X
 0  X X^3+X^2+X X^2+X  0 X^3+X^2 X^3  0 X^3+X^2+X X^2  X X^2+X X^3+X^2+X X^2 X^2 X^3+X  0
 0  0 X^3+X^2  0  0 X^3 X^2 X^2 X^2  0 X^3+X^2 X^3 X^3+X^2 X^2 X^3+X^2 X^3  0
 0  0  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3
 0  0  0  0 X^3  0 X^3  0  0 X^3  0 X^3  0 X^3  0 X^3 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+164x^14+64x^15+629x^16+384x^17+584x^18+64x^19+128x^20+20x^22+10x^24

The gray image is a linear code over GF(2) with n=136, k=11 and d=56.
This code was found by Heurico 1.16 in 11.9 seconds.