The generator matrix

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

generates a code of length 10 over Z2[X]/(X^4) who´s minimum homogenous weight is 7.

Homogenous weight enumerator: w(x)=1x^0+74x^7+305x^8+794x^9+1764x^10+786x^11+286x^12+70x^13+12x^14+4x^15

The gray image is a linear code over GF(2) with n=80, k=12 and d=28.
This code was found by Heurico 1.16 in 0.016 seconds.