The generator matrix
1 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
0 X 0 0 0 0 0 0 0 X X X X X X X 0 0 0 0 0 X X X X 0 X 0 X 0 X 0 X 0 0 X
0 0 X 0 0 0 X X X X X 0 X X 0 0 0 0 0 0 X X 0 0 0 X X X X X X X X 0 0 0
0 0 0 X 0 X X X 0 0 0 0 X X X X 0 0 X X X 0 X 0 0 X 0 0 0 0 X X X 0 X X
0 0 0 0 X X 0 X X 0 X X X 0 0 X 0 X X 0 0 0 X X 0 0 X X 0 0 X X 0 X X 0
generates a code of length 36 over Z2[X]/(X^2) who´s minimum homogenous weight is 34.
Homogenous weight enumerator: w(x)=1x^0+20x^34+27x^36+8x^38+3x^40+2x^42+1x^44+2x^50
The gray image is a linear code over GF(2) with n=72, k=6 and d=34.
This code was found by Heurico 1.16 in 0.174 seconds.