The generator matrix

 1  0  0  0  0  0  0  1  1  1  1  1  1  X  1  X  1  1  1  0  1  0  1  1  1  1  1  0  1  1
 0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  1  1  X  1  X  X X+1  1  1 X+1  X  1  X
 0  0  1  0  0  0  0  0  0  1  1  X X+1  1 X+1  1 X+1  X  X  1  1  1  X X+1  X X+1  0  1  0  1
 0  0  0  1  0  0  0  0  1  0  X X+1  1  1 X+1  X  X X+1  1  0 X+1  0  1  X  1  1  0 X+1 X+1  X
 0  0  0  0  1  0  0  0  1  1  0 X+1  0 X+1 X+1  X  X  0 X+1  X  X  1  1  1  X  1  1  0  X  X
 0  0  0  0  0  1  0  1  0 X+1  X  X X+1  0  X  1  1  1  X  1  0  X  1  1  0  0  0 X+1 X+1  1
 0  0  0  0  0  0  1  1 X+1  X X+1  X  X  1  X X+1  0  1  1  0  1  1  0  1  0  X X+1  X  X  X
 0  0  0  0  0  0  0  X  X  0  X  0  0  0  X  0  X  0  0  X  X  0  X  X  0  0  0  0  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+145x^20+286x^21+536x^22+712x^23+1055x^24+1412x^25+1832x^26+2468x^27+2813x^28+3220x^29+3446x^30+3400x^31+2977x^32+2576x^33+2012x^34+1392x^35+947x^36+638x^37+464x^38+208x^39+119x^40+60x^41+28x^42+12x^43+7x^44+2x^46

The gray image is a linear code over GF(2) with n=60, k=15 and d=20.
This code was found by Heurico 1.11 in 16.5 seconds.