The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  0  X  0  1  1  0  1  0  1  X  0  1  0  1  0  1  0  1  X
 0  1  0  1  0  1  1  0  0  1  1  1  1  X  X  X  0  1  1 X+1  1  0  0  1 X+1  0  1  1  X  0
 0  0  1  1  1  0  1  0  1  1  0  X  1  1  1  0  1  1  0  0 X+1  1  0  0  X  1  0 X+1  1  X
 0  0  0  X  0  0  0  0  0  0  0  X  0  X  0  X  0  0  X  0  0  0  0  X  X  0  X  X  0  X
 0  0  0  0  X  0  0  0  0  0  0  X  X  0  X  X  0  X  X  0  0  X  X  0  0  X  X  X  0  0
 0  0  0  0  0  X  0  0  0  0  0  0  X  X  0  X  0  X  X  X  0  X  0  0  X  0  0  X  X  X
 0  0  0  0  0  0  X  0  0  0  0  0  X  0  0  0  0  0  0  X  X  X  X  X  X  0  X  X  0  0
 0  0  0  0  0  0  0  X  0  0  0  0  0  0  X  0  0  0  X  0  X  0  X  0  X  X  X  X  X  0
 0  0  0  0  0  0  0  0  X  0  0  X  X  0  X  X  X  0  0  X  X  0  X  0  X  0  0  0  0  0
 0  0  0  0  0  0  0  0  0  X  0  X  0  X  0  X  X  X  0  X  X  0  X  X  X  X  X  X  X  X
 0  0  0  0  0  0  0  0  0  0  X  0  X  X  0  X  X  0  0  0  X  X  0  X  0  0  0  X  X  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+224x^20+318x^22+1252x^24+1670x^26+3055x^28+3180x^30+3277x^32+1708x^34+1211x^36+278x^38+172x^40+14x^42+21x^44+2x^48+1x^52

The gray image is a linear code over GF(2) with n=60, k=14 and d=20.
This code was found by Heurico 1.16 in 36.7 seconds.