The generator matrix

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

generates a code of length 11 over Z2[X]/(X^4) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+86x^10+80x^11+87x^12+1x^14+1x^18

The gray image is a linear code over GF(2) with n=88, k=8 and d=40.
As d=41 is an upper bound for linear (88,8,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 8.
This code was found by Heurico 1.16 in 3.62e-008 seconds.