The generator matrix

 1  0  0  0  0  1  1  1  0  1  1  X  1  X  1  X  1  X  1  1  X  1  1  X  1  X  1  0  1  X
 0  1  0  0  0  0  0  0  0  1 X+1  1  1  1 X+1  1  1  1  X  1  X  1  X  1  1  1  X  0  X  1
 0  0  1  0  0  0  1  1  1  1  1  0  0  X  1  1  0  1 X+1  0  1  1  X X+1  X  0 X+1  1 X+1  0
 0  0  0  1  0  1  1  0  1  0  0  1 X+1  X X+1  1  0  X  1  0 X+1 X+1  1  X X+1 X+1  X  1  0  1
 0  0  0  0  1  1  0  1  1  0  1  0  X  1  0 X+1  1  X X+1  X  X X+1  0 X+1 X+1 X+1  X  X X+1  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  X  X
 0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  X  X  X  0  0  X  X  X  0  X  X  X  0
 0  0  0  0  0  0  0  X  0  0  0  0  0  0  X  X  X  X  X  0  X  0  0  X  X  X  X  X  0  0
 0  0  0  0  0  0  0  0  X  0  X  X  X  0  X  X  X  X  0  0  X  X  X  X  X  0  X  X  0  X
 0  0  0  0  0  0  0  0  0  X  X  0  X  X  X  0  0  0  0  0  X  X  0  X  0  X  0  0  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+267x^20+914x^22+2176x^24+3688x^26+5871x^28+6668x^30+6179x^32+3864x^34+2113x^36+690x^38+268x^40+48x^42+21x^44

The gray image is a linear code over GF(2) with n=60, k=15 and d=20.
This code was found by Heurico 1.16 in 37.7 seconds.