The generator matrix

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

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+16x^30+8x^31+5x^32+2x^36

The gray image is a linear code over GF(2) with n=240, k=5 and d=120.
As d=123 is an upper bound for linear (240,5,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 5.
This code was found by Heurico 1.16 in 3.81e-009 seconds.