The generator matrix

 1  1  1  1  1  1  1  1  1  1
 0 X^3  0  0  0 X^3  0  0 X^3 X^3
 0  0 X^3  0  0 X^3  0 X^3 X^3  0
 0  0  0 X^3  0 X^3 X^3 X^3  0  0
 0  0  0  0 X^3 X^3 X^3  0  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+15x^8+224x^10+15x^12+1x^20

The gray image is a linear code over GF(2) with n=80, k=8 and d=32.
This code was found by Heurico 1.16 in -1.01e-007 seconds.