The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X X X X X 0 0 0 0 0 0 0 1 1 X 1 1 1 1 1
0 X 0 0 0 X X X 0 0 0 X 0 X X X 0 0 X X 0 X X X X X X 0 0 0 0 0 0 0 X 0 X X
0 0 X 0 X X X 0 0 0 X X X X 0 0 0 X X 0 X X 0 0 0 X X X X 0 0 0 0 X X X X 0
0 0 0 X X 0 X X 0 X X 0 0 X X 0 X X 0 0 0 X X 0 X X 0 0 X X 0 X 0 X 0 0 X X
generates a code of length 38 over Z2[X]/(X^2) who´s minimum homogenous weight is 38.
Homogenous weight enumerator: w(x)=1x^0+7x^38+16x^39+7x^40+1x^46
The gray image is a linear code over GF(2) with n=76, k=5 and d=38.
As d=38 is an upper bound for linear (76,5,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 5.
This code was found by Heurico 1.16 in 0.00559 seconds.