The generator matrix
1 1 1 1 1 1 1 1 X 1 1 X 1 X 1 X^2 X X X X^2 X^2 X^3 0 1
0 X^3 0 X^3 0 X^3 0 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 0 X^3 0 0 X^3 X^3 X^3 0
generates a code of length 24 over Z2[X]/(X^4) who´s minimum homogenous weight is 24.
Homogenous weight enumerator: w(x)=1x^0+16x^24+10x^25+2x^26+2x^27+1x^28
The gray image is a linear code over GF(2) with n=192, k=5 and d=96.
As d=98 is an upper bound for linear (192,5,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 5.
This code was found by Heurico 1.16 in 6.87e-008 seconds.