The generator matrix

 1  1  1  1  X X^3  1  1  X  1
 0  X  0 X^3+X^2+X X^2+X  X X^3+X^2 X^2+X X^3+X^2+X X^3
 0  0 X^3+X^2  0  0 X^3 X^2 X^3+X^2 X^2  0
 0  0  0 X^3+X^2  0 X^3+X^2 X^2 X^2 X^3 X^2
 0  0  0  0 X^3 X^3  0  0 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+20x^6+104x^7+231x^8+1048x^9+1288x^10+1048x^11+231x^12+104x^13+20x^14+1x^20

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 0.016 seconds.