The generator matrix

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

generates a code of length 30 over Z2[X]/(X^2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+506x^16+224x^18+1152x^22+1544x^24+1568x^26+2045x^28+2304x^30+2045x^32+1568x^34+1544x^36+1152x^38+224x^42+506x^44+1x^60

The gray image is a linear code over GF(2) with n=60, k=14 and d=16.
This code was found by Heurico 1.16 in 6.93 seconds.