The generator matrix

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

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+88x^20+164x^22+607x^24+810x^26+1601x^28+1608x^30+1657x^32+868x^34+538x^36+132x^38+103x^40+2x^42+13x^44

The gray image is a linear code over GF(2) with n=60, k=13 and d=20.
This code was found by Heurico 1.16 in 2.57 seconds.