The generator matrix

 1  0  0  0  0  0  1  1  1  0  1  X  1  0  1  1  X  X  1  X  1  0  1  1  0  0  1  X  1  1
 0  1  0  0  0  0  0  0  0  0  0  0  X  X X+1 X+1  1  1  1  1  1  1  X  1  X  1 X+1  1  1  X
 0  0  1  0  0  0  0  0  X  X  1  1 X+1  1  X X+1  0 X+1  X  0  1 X+1 X+1 X+1  0  X X+1  X  X  0
 0  0  0  1  0  0  X  1 X+1  1  0  1  1 X+1  0  X  1  0  X  X  X X+1 X+1  0  1  1 X+1  X X+1  0
 0  0  0  0  1  0 X+1  1  0  1  X X+1  0  X  X  0  1 X+1  1  0 X+1  1 X+1 X+1  0  X  X  0  0  0
 0  0  0  0  0  1  1  X  1  1 X+1  X  X  1  X X+1  1 X+1  1 X+1  X  X  1  X X+1 X+1  0  X  X X+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+38x^22+124x^23+174x^24+242x^25+284x^26+278x^27+358x^28+362x^29+330x^30+374x^31+412x^32+342x^33+258x^34+226x^35+120x^36+78x^37+48x^38+22x^39+20x^40+2x^42+2x^44+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 1.16 in 0.734 seconds.