The generator matrix

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

generates a code of length 10 over Z2[X]/(X^4) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+125x^8+204x^9+392x^10+168x^11+114x^12+12x^13+8x^14

The gray image is a linear code over GF(2) with n=80, k=10 and d=32.
This code was found by Heurico 1.16 in 0.031 seconds.