The generator matrix

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

generates a code of length 23 over Z2[X]/(X^4) who´s minimum homogenous weight is 23.

Homogenous weight enumerator: w(x)=1x^0+20x^23+4x^24+4x^25+2x^26+1x^28

The gray image is a linear code over GF(2) with n=184, k=5 and d=92.
As d=94 is an upper bound for linear (184,5,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 5.
This code was found by Heurico 1.16 in 0.015 seconds.