The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+29x^4+24x^6+194x^8+1552x^10+194x^12+24x^14+29x^16+1x^20

The gray image is a linear code over GF(2) with n=80, k=11 and d=16.
This code was found by Heurico 1.16 in -3.24e-008 seconds.