The generator matrix

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

generates a code of length 10 over Z2[X]/(X^4) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+61x^8+108x^9+200x^10+72x^11+50x^12+12x^13+8x^14

The gray image is a linear code over GF(2) with n=80, k=9 and d=32.
This code was found by Heurico 1.16 in 3.62e-008 seconds.