The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  X  X  X  1  X  1  X  1  1  1  0  1  0  0  1  1  0  X
 0  1  0  0  0  1  1  1  X  0 X+1 X+1  1  1  X  1  1 X+1  1  0  0  X  1 X+1  X  0  X  X  0  0
 0  0  1  0  1  1  0  1  0 X+1 X+1  X  X X+1  1  1  X  0  0  0  1  0 X+1  X  1  1  0  1  X  X
 0  0  0  1  1  0  1  1  1  0  1  X X+1  0  1 X+1  X  X  1  0  X  1  1  0  1 X+1  0  1  1  X
 0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  0  X  X
 0  0  0  0  0  X  0  0  0  0  0  0  X  0  X  X  X  X  X  0  X  X  X  0  0  0  X  0  X  X
 0  0  0  0  0  0  X  0  0  0  0  0  0  X  X  X  X  0  0  X  0  X  X  X  X  0  0  X  X  X
 0  0  0  0  0  0  0  X  X  X  0  X  X  X  X  X  X  X  X  X  0  0  X  0  X  X  0  X  0  0

generates a code of length 30 over Z2[X]/(X^2) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+115x^22+330x^24+550x^26+670x^28+719x^30+763x^32+560x^34+256x^36+93x^38+26x^40+10x^42+2x^44+1x^46

The gray image is a linear code over GF(2) with n=60, k=12 and d=22.
This code was found by Heurico 1.16 in 0.73 seconds.