The generator matrix
1 1 1 1 1 1 X^3 X X 1
0 X 0 X X^3 0 X^2 X X^3+X X^2
0 0 X X X^2 X^2+X X X 0 X^3+X^2
0 0 0 X^3 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 7.
Homogenous weight enumerator: w(x)=1x^0+38x^7+194x^8+412x^9+772x^10+408x^11+172x^12+36x^13+12x^14+2x^15+1x^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 -1.01e-007 seconds.