The generator matrix
1 1 1 1 1 1 1 1 X 1 X 1 X X 1 X 1 X 1 X X X X X X X X 1 X
0 X 0 0 0 0 0 X X 0 X 0 X X X X X 0 X 0 0 X 0 X X 0 0 X 0
0 0 X 0 0 0 X 0 X X X X X X X 0 X 0 X X X 0 0 0 0 0 X 0 0
0 0 0 X 0 X X X 0 X X 0 0 X 0 X 0 X X X 0 X 0 0 0 X X 0 0
0 0 0 0 X X 0 0 X X X X 0 0 0 0 X X X 0 0 X X X 0 0 X X 0
generates a code of length 29 over Z2[X]/(X^2) who´s minimum homogenous weight is 28.
Homogenous weight enumerator: w(x)=1x^0+38x^28+16x^30+7x^32+2x^44
The gray image is a linear code over GF(2) with n=58, k=6 and d=28.
As d=28 is an upper bound for linear (58,6,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 6.
This code was found by Heurico 1.16 in 0.116 seconds.