The generator matrix

 1  0  1  1  1 X^3+X  1  1 X^3+X^2  1
 0  1  1 X^2 X^3+X^2+X+1  1 X^3+X+1 X^3+X^2+X  1 X^2+X
 0  0  X X^3+X X^2+X X^3 X^2 X^3+X^2 X^3+X^2+X  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+164x^8+474x^9+801x^10+444x^11+139x^12+10x^13+15x^14

The gray image is a linear code over GF(2) with n=80, k=11 and d=32.
As d=35 is an upper bound for linear (80,11,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 11.
This code was found by Heurico 1.16 in 0.016 seconds.