The generator matrix

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

generates a code of length 17 over Z2[X]/(X^4) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+58x^12+56x^14+64x^15+537x^16+640x^17+496x^18+64x^19+92x^20+24x^22+14x^24+2x^28

The gray image is a linear code over GF(2) with n=136, k=11 and d=48.
This code was found by Heurico 1.16 in 0.015 seconds.