The generator matrix

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

generates a code of length 10 over Z2[X]/(X^4) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+16x^9+28x^10+16x^11+2x^12+1x^16

The gray image is a linear code over GF(2) with n=80, k=6 and d=36.
This code was found by Heurico 1.16 in 3.81e-009 seconds.