The generator matrix
1 1 1 1 1 1 1 X 1 X X X X^2 0 X^2 X^2 1
0 X^3+X^2 X^3 X^2 0 X^3+X^2 X^3 X^3+X^2 X^2 X^2 0 X^3 X^3+X^2 X^2 X^3 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+19x^16+16x^17+20x^18+8x^19
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 0.016 seconds.