The generator matrix

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

generates a code of length 3 over Z2[X]/(X^4) who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+23x^2+80x^3+23x^4+1x^6

The gray image is a linear code over GF(2) with n=24, k=7 and d=8.
As d=10 is an upper bound for linear (24,7,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 7.
This code was found by Heurico 1.16 in 6.87e-008 seconds.