The generator matrix

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

generates a code of length 10 over Z2[X]/(X^4) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+32x^6+32x^7+169x^8+604x^9+361x^10+620x^11+178x^12+20x^13+22x^14+4x^15+4x^16+1x^18

The gray image is a linear code over GF(2) with n=80, k=11 and d=24.
This code was found by Heurico 1.16 in -6.48e-008 seconds.