The generator matrix

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

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+50x^12+4x^13+82x^14+100x^15+663x^16+216x^17+670x^18+152x^19+54x^20+36x^21+14x^22+4x^23+2x^26

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.