The generator matrix

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

generates a code of length 19 over Z2[X]/(X^4) who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+84x^17+94x^18+152x^19+94x^20+84x^21+2x^22+1x^32

The gray image is a linear code over GF(2) with n=152, k=9 and d=68.
This code was found by Heurico 1.16 in 0.016 seconds.