The generator matrix

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

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+162x^8+704x^10+152x^12+5x^16

The gray image is a linear code over GF(2) with n=80, k=10 and d=32.
This code was found by Heurico 1.16 in -3.24e-008 seconds.