The generator matrix

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

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+94x^8+32x^9+212x^10+128x^11+40x^12+4x^14+1x^16

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 6.87e-008 seconds.