The generator matrix

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

generates a code of length 17 over Z2[X]/(X^4) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+54x^13+96x^14+242x^15+429x^16+444x^17+416x^18+228x^19+48x^20+46x^21+32x^22+10x^23+2x^24

The gray image is a linear code over GF(2) with n=136, k=11 and d=52.
This code was found by Heurico 1.16 in 0.031 seconds.