The generator matrix

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

generates a code of length 30 over Z2[X]/(X^4) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+48x^30+15x^32

The gray image is a linear code over GF(2) with n=240, k=6 and d=120.
As d=120 is an upper bound for linear (240,6,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 6.
This code was found by Heurico 1.16 in -6.48e-008 seconds.