The generator matrix

 1  1  1  1  1  1  1  1  X  1
 0  X  0  X X^3 X^3+X^2 X^2+X X^3+X  X  0
 0  0  X  X  0  X X^2+X X^3+X^2 X^2+X  0
 0  0  0 X^2 X^3+X^2 X^3+X^2 X^3 X^3+X^2 X^2  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+40x^6+118x^7+183x^8+780x^9+1857x^10+776x^11+182x^12+116x^13+38x^14+2x^15+2x^16+1x^18

The gray image is a linear code over GF(2) with n=80, k=12 and d=24.
This code was found by Heurico 1.16 in 0.031 seconds.