The generator matrix

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

generates a code of length 10 over Z2[X]/(X^4) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+84x^9+85x^10+84x^11+1x^14+1x^16

The gray image is a linear code over GF(2) with n=80, k=8 and d=36.
As d=37 is an upper bound for linear (80,8,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 8.
This code was found by Heurico 1.16 in 1.05e-007 seconds.