The generator matrix

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

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+98x^7+641x^8+1538x^9+3652x^10+1530x^11+622x^12+94x^13+12x^14+4x^15

The gray image is a linear code over GF(2) with n=80, k=13 and d=28.
This code was found by Heurico 1.16 in 0.094 seconds.