The generator matrix

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

generates a code of length 30 over Z2[X]/(X^2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+82x^20+36x^22+327x^24+368x^26+872x^28+728x^30+878x^32+368x^34+314x^36+36x^38+73x^40+12x^44+1x^48

The gray image is a linear code over GF(2) with n=60, k=12 and d=20.
This code was found by Heurico 1.16 in 0.79 seconds.