The generator matrix

 1  1  1  1  1  1  1  1  X X^3  0  1 X^3+X^2  1  1  1  0
 0  X  0 X^3+X^2+X X^2 X^2+X X^3+X^2+X X^3 X^2+X  X  X  0  X X^3+X  X X^3  X
 0  0 X^3+X^2  0 X^2  0 X^2 X^3 X^3+X^2 X^3  0 X^2 X^3 X^3+X^2 X^3+X^2  0 X^3+X^2
 0  0  0 X^3+X^2  0  0 X^3 X^3+X^2 X^2 X^2 X^3 X^3+X^2  0 X^2 X^2 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 X^3  0  0 X^3  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+66x^13+196x^14+388x^15+829x^16+1150x^17+856x^18+376x^19+128x^20+62x^21+36x^22+4x^23+2x^24+2x^25

The gray image is a linear code over GF(2) with n=136, k=12 and d=52.
This code was found by Heurico 1.16 in 14.5 seconds.