The generator matrix

 1  0  0  0  0  0  0  1  1  1  0  1  1  X  1  1  0  0  X  1  1  0  1  1  X  1  X  X  1  1
 0  1  0  0  0  0  0  X  X X+1  1 X+1  1  1  0  1  X  X  0  X  X  1  X X+1  X X+1  0  1  1  0
 0  0  1  0  0  0  0  0  0  0  0  0  0 X+1  1 X+1  X  1  X  1  X  X  1  X  1  1  X X+1  0  0
 0  0  0  1  0  0  0  0 X+1  1  X X+1  X X+1  1  X  1  0  X  X X+1  0 X+1 X+1  1  1  1  X  1  0
 0  0  0  0  1  0  0  1 X+1  0  X  0  1  1 X+1  X  1  1  1  1 X+1  1  X  1  0  0  0  1  0  0
 0  0  0  0  0  1  0  1  X  X  1 X+1 X+1  1 X+1  X  X  0 X+1  0  1  0  0 X+1  X  0  0  X  0  0
 0  0  0  0  0  0  1  1  0 X+1  1  X  0  0  X X+1  1 X+1 X+1  X  X  1  0  X  1  X  1  1  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+83x^20+102x^21+370x^22+392x^23+602x^24+682x^25+911x^26+1254x^27+1307x^28+1608x^29+1517x^30+1710x^31+1466x^32+1332x^33+991x^34+694x^35+540x^36+282x^37+277x^38+106x^39+95x^40+26x^41+30x^42+4x^43+2x^44

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 20.8 seconds.