The generator matrix

 1  1  1  1  1  1  1
 0  X X^3+X^2 X^2+X X^3 X^3+X^2+X 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+7x^6+112x^7+7x^8+1x^14

The gray image is a linear code over GF(2) with n=56, k=7 and d=24.
As d=26 is an upper bound for linear (56,7,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 7.
This code was found by Heurico 1.16 in 1.05e-007 seconds.