The generator matrix

 1  1  1  1  1  1  1  1  X  X  0
 0  X X^3+X^2 X^2+X  0 X^3+X^2+X X^3 X^3+X X^2 X^2+X  X
 0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 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+103x^10+64x^11+78x^12+8x^14+1x^16+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 0.016 seconds.