The generator matrix

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

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+49x^20+118x^21+247x^22+438x^23+527x^24+728x^25+1008x^26+1202x^27+1296x^28+1560x^29+1835x^30+1600x^31+1449x^32+1356x^33+1032x^34+728x^35+457x^36+306x^37+221x^38+122x^39+55x^40+28x^41+8x^42+6x^43+6x^44+1x^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 19 seconds.