The generator matrix
1 1 1 1 1 1 1 1 1 X 1 X X X X X X 1 1 1 1 X 1 1 1
0 X^3 0 0 0 X^3 X^3 X^3 0 0 0 X^3 X^3 0 X^3 X^3 0 0 X^3 0 X^3 0 X^3 X^3 0
0 0 X^3 0 X^3 X^3 X^3 0 0 0 X^3 X^3 0 X^3 X^3 0 X^3 0 X^3 X^3 X^3 0 0 0 0
0 0 0 X^3 X^3 0 X^3 X^3 0 X^3 X^3 0 0 0 X^3 X^3 X^3 X^3 0 0 X^3 0 X^3 0 0
generates a code of length 25 over Z2[X]/(X^4) who´s minimum homogenous weight is 24.
Homogenous weight enumerator: w(x)=1x^0+7x^24+110x^25+7x^26+2x^33+1x^34
The gray image is a linear code over GF(2) with n=200, k=7 and d=96.
As d=99 is an upper bound for linear (200,7,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 7.
This code was found by Heurico 1.16 in 0.016 seconds.