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.