The generator matrix

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

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+66x^22+94x^23+186x^24+262x^25+242x^26+312x^27+274x^28+356x^29+398x^30+376x^31+430x^32+328x^33+262x^34+212x^35+126x^36+76x^37+56x^38+26x^39+6x^40+2x^41+4x^43+1x^48

The gray image is a linear code over GF(2) with n=60, k=12 and d=22.
This code was found by Heurico 1.10 in 0.281 seconds.