The generator matrix

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

generates a code of length 30 over Z2[X]/(X^2) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+84x^22+116x^23+171x^24+228x^25+285x^26+294x^27+327x^28+356x^29+309x^30+414x^31+346x^32+348x^33+279x^34+178x^35+164x^36+92x^37+59x^38+22x^39+14x^40+8x^42+1x^52

The gray image is a linear code over GF(2) with n=60, k=12 and d=22.
This code was found by Heurico 1.16 in 0.713 seconds.