The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X 0 X X X X 0 0 0 0 0 0
0 X 0 0 0 X X X 0 0 0 X 0 X X 0 0 X X 0 X X X X X X 0 0 0
0 0 X 0 X X X 0 0 0 X X X X 0 0 X X 0 X X 0 0 0 X X X X 0
0 0 0 X X 0 X X 0 X X 0 0 X X X X 0 0 0 X 0 X X X 0 0 X X
generates a code of length 29 over Z2[X]/(X^2) who´s minimum homogenous weight is 29.
Homogenous weight enumerator: w(x)=1x^0+16x^29+8x^30+7x^32
The gray image is a linear code over GF(2) with n=58, k=5 and d=29.
As d=29 is an upper bound for linear (58,5,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 5.
This code was found by Heurico 1.16 in 0.0152 seconds.