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  1  1  1  1  1  1  1  1  1
 0  X  0  0  0  0  0  0  0  X  X  X  X  X  X  X  0  0  0  0  X  X  0  0  X  X  0  0  X  X  X
 0  0  X  0  0  0  X  X  X  X  X  0  X  X  0  0  0  0  0  X  X  0  0  X  X  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  X  X  0  0  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  0  X  X  0  X  0  X  0  X

generates a code of length 31 over Z2[X]/(X^2) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+15x^30+32x^31+15x^32+1x^62

The gray image is a linear code over GF(2) with n=62, k=6 and d=30.
This code was found by Heurico 1.16 in 0.0049 seconds.