The generator matrix

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

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+32x^13+16x^14+126x^16+704x^17+96x^18+32x^21+16x^22+1x^32

The gray image is a linear code over GF(2) with n=136, k=10 and d=52.
This code was found by Heurico 1.16 in 12.6 seconds.