The generator matrix
1 0 1 1 1 1 1 1 1 0
0 1 X+1 X^2+X X^2+1 X^3+X^2 X^3+X^2+X+1 X^3+X X^2+1 X
0 0 X^3 0 0 0 X^3 X^3 X^3 X^3
0 0 0 X^3 0 X^3 X^3 X^3 0 X^3
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 7.
Homogenous weight enumerator: w(x)=1x^0+20x^7+162x^8+480x^9+704x^10+520x^11+152x^12+4x^15+5x^16
The gray image is a linear code over GF(2) with n=80, k=11 and d=28.
This code was found by Heurico 1.16 in 0.141 seconds.