The generator matrix

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

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+36x^7+322x^8+796x^9+1823x^10+750x^11+309x^12+48x^13+9x^14+2x^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.