The generator matrix

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

generates a code of length 17 over Z2[X]/(X^4) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+22x^14+142x^15+181x^16+390x^17+147x^18+74x^19+26x^20+34x^21+6x^22+1x^26

The gray image is a linear code over GF(2) with n=136, k=10 and d=56.
This code was found by Heurico 1.16 in -6.48e-008 seconds.