The generator matrix

 1  1  1  1  1  1  1  1  1  X X^2  1  1  1  X  X  1
 0 X^3+X^2  0 X^2  0  0 X^2 X^2 X^3 X^3 X^3  0 X^2 X^3+X^2 X^2 X^3+X^2  0
 0  0 X^3+X^2 X^2  0 X^3+X^2 X^3+X^2  0 X^3 X^2 X^2  0 X^2 X^3 X^3+X^2  0  0
 0  0  0 X^3  0  0 X^3  0  0 X^3  0 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  0  0 X^3 X^3  0
 0  0  0  0  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3  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+36x^12+32x^13+60x^14+128x^15+417x^16+704x^17+419x^18+128x^19+52x^20+32x^21+31x^22+6x^24+1x^26+1x^30

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 0.016 seconds.