The generator matrix

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

generates a code of length 7 over Z2[X]/(X^4) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+78x^6+96x^7+79x^8+2x^10

The gray image is a linear code over GF(2) with n=56, k=8 and d=24.
As d=24 is an upper bound for linear (56,8,2)-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.