The generator matrix

 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
 0  X  0  0  0  0  0  X  0  X  X  0  X  X  X  0  0  0  X  X  0  0  X  X  0  0  X  X  X  X
 0  0  X  0  0  0  X  0  X  X  X  X  X  X  0  0  0  X  X  0  0  X  X  0  X  X  X  X  0  0
 0  0  0  X  0  X  X  X  X  0  0  0  X  X  X  0  X  X  0  0  X  X  X  X  0  0  0  X  X  0
 0  0  0  0  X  X  0  0  X  0  X  X  X  0  X  X  X  0  0  0  0  X  X  0  X  0  X  0  X  X

generates a code of length 30 over Z2[X]/(X^2) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+30x^29+16x^30+15x^32+2x^45

The gray image is a linear code over GF(2) with n=60, k=6 and d=29.
This code was found by Heurico 1.16 in 0.39 seconds.