The generator matrix

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

generates a code of length 30 over Z2[X]/(X^2) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+52x^21+142x^22+186x^23+328x^24+404x^25+462x^26+618x^27+652x^28+756x^29+879x^30+812x^31+741x^32+668x^33+458x^34+388x^35+298x^36+152x^37+98x^38+42x^39+26x^40+16x^41+8x^42+2x^43+2x^44+1x^46

The gray image is a linear code over GF(2) with n=60, k=13 and d=21.
This code was found by Heurico 1.16 in 2.84 seconds.