The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X X X X X X X X X X X X X 1
0 X 0 0 0 0 0 0 0 X X X X X X X 0 0 0 0 X 0 X X X X 0 0 X 0 X 0 0 X 0 X X
0 0 X 0 0 0 X X X X X 0 X X 0 0 0 0 0 X X X X 0 0 0 0 X X 0 0 0 X X X X 0
0 0 0 X 0 X X X 0 0 0 0 X X X X 0 0 X X 0 0 X X 0 0 0 0 0 X X X X 0 X X 0
0 0 0 0 X X 0 X X 0 X X X 0 0 X 0 X X 0 0 0 0 X X 0 X X 0 0 0 X X X 0 X 0
generates a code of length 37 over Z2[X]/(X^2) who´s minimum homogenous weight is 36.
Homogenous weight enumerator: w(x)=1x^0+45x^36+15x^40+1x^44+2x^52
The gray image is a linear code over GF(2) with n=74, k=6 and d=36.
As d=36 is an upper bound for linear (74,6,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 6.
This code was found by Heurico 1.16 in 4.74 seconds.