The generator matrix

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

generates a code of length 31 over Z2[X]/(X^2) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+81x^22+106x^23+221x^24+302x^25+398x^26+512x^27+620x^28+710x^29+743x^30+800x^31+719x^32+760x^33+596x^34+540x^35+424x^36+264x^37+215x^38+86x^39+57x^40+10x^41+14x^42+4x^43+4x^44+2x^45+1x^46+2x^48

The gray image is a linear code over GF(2) with n=62, k=13 and d=22.
This code was found by Heurico 1.16 in 3.09 seconds.