The generator matrix

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

generates a code of length 17 over Z2[X]/(X^4) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+3x^16+52x^17+4x^18+4x^21

The gray image is a linear code over GF(2) with n=136, k=6 and d=64.
This code was found by Heurico 1.16 in -6.48e-008 seconds.