The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  X  X  X  1  0  1  1  X  1  X  1  1  1  X  0  0  1  1
 0  1  0  0  0  1  1  1  0  0 X+1 X+1  1  0  1  X  0 X+1  0  X  X  X  1 X+1  0  1  1  1  X  0
 0  0  1  0  1  1  0  1  0  1  1  0  0  1  1  1  1 X+1 X+1  1  X  0  0  1  X  1 X+1  X  0  0
 0  0  0  1  1  0  1  1  1  0  1  0  1  1  0  0  X X+1  1 X+1  X  1  X  0  1  1 X+1  1  0  0
 0  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  0  X  X  0
 0  0  0  0  0  X  0  0  0  0  0  X  0  X  X  0  X  X  0  X  X  X  X  X  X  X  X  X  X  0
 0  0  0  0  0  0  X  0  0  0  X  X  0  X  X  0  X  0  X  0  X  X  0  0  0  X  0  X  X  0
 0  0  0  0  0  0  0  X  0  0  X  0  X  0  X  0  X  X  X  X  X  0  X  X  0  0  0  X  0  0
 0  0  0  0  0  0  0  0  X  0  X  X  X  X  0  X  X  X  0  0  0  X  0  X  0  0  0  0  0  0
 0  0  0  0  0  0  0  0  0  X  0  0  0  0  X  X  0  X  X  X  0  X  0  0  X  X  X  0  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+147x^20+84x^21+313x^22+346x^23+630x^24+692x^25+907x^26+1202x^27+1321x^28+1728x^29+1484x^30+1772x^31+1359x^32+1312x^33+1054x^34+684x^35+557x^36+268x^37+281x^38+90x^39+74x^40+12x^41+55x^42+2x^43+7x^44+2x^46

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 18.9 seconds.